Diff for /imach/src/imach.c between versions 1.32 and 1.126

version 1.32, 2002/03/11 14:17:15 version 1.126, 2006/04/28 17:23:28
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.126  2006/04/28 17:23:28  brouard
      (Module): Yes the sum of survivors was wrong since
   This program computes Healthy Life Expectancies from    imach-114 because nhstepm was no more computed in the age
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    loop. Now we define nhstepma in the age loop.
   first survey ("cross") where individuals from different ages are    Version 0.98h
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.125  2006/04/04 15:20:31  lievre
   second wave of interviews ("longitudinal") which measure each change    Errors in calculation of health expectancies. Age was not initialized.
   (if any) in individual health status.  Health expectancies are    Forecasting file added.
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.124  2006/03/22 17:13:53  lievre
   Maximum Likelihood of the parameters involved in the model.  The    Parameters are printed with %lf instead of %f (more numbers after the comma).
   simplest model is the multinomial logistic model where pij is the    The log-likelihood is printed in the log file
   probabibility to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.123  2006/03/20 10:52:43  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    * imach.c (Module): <title> changed, corresponds to .htm file
   'age' is age and 'sex' is a covariate. If you want to have a more    name. <head> headers where missing.
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    * imach.c (Module): Weights can have a decimal point as for
   you to do it.  More covariates you add, slower the    English (a comma might work with a correct LC_NUMERIC environment,
   convergence.    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
   The advantage of this computer programme, compared to a simple    1.
   multinomial logistic model, is clear when the delay between waves is not    Version 0.98g
   identical for each individual. Also, if a individual missed an  
   intermediate interview, the information is lost, but taken into    Revision 1.122  2006/03/20 09:45:41  brouard
   account using an interpolation or extrapolation.      (Module): Weights can have a decimal point as for
     English (a comma might work with a correct LC_NUMERIC environment,
   hPijx is the probability to be observed in state i at age x+h    otherwise the weight is truncated).
   conditional to the observed state i at age x. The delay 'h' can be    Modification of warning when the covariates values are not 0 or
   split into an exact number (nh*stepm) of unobserved intermediate    1.
   states. This elementary transition (by month or quarter trimester,    Version 0.98g
   semester or year) is model as a multinomial logistic.  The hPx  
   matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.121  2006/03/16 17:45:01  lievre
   and the contribution of each individual to the likelihood is simply    * imach.c (Module): Comments concerning covariates added
   hPijx.  
     * imach.c (Module): refinements in the computation of lli if
   Also this programme outputs the covariance matrix of the parameters but also    status=-2 in order to have more reliable computation if stepm is
   of the life expectancies. It also computes the prevalence limits.    not 1 month. Version 0.98f
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.120  2006/03/16 15:10:38  lievre
            Institut national d'études démographiques, Paris.    (Module): refinements in the computation of lli if
   This software have been partly granted by Euro-REVES, a concerted action    status=-2 in order to have more reliable computation if stepm is
   from the European Union.    not 1 month. Version 0.98f
   It is copyrighted identically to a GNU software product, ie programme and  
   software can be distributed freely for non commercial use. Latest version    Revision 1.119  2006/03/15 17:42:26  brouard
   can be accessed at http://euroreves.ined.fr/imach .    (Module): Bug if status = -2, the loglikelihood was
   **********************************************************************/    computed as likelihood omitting the logarithm. Version O.98e
    
 #include <math.h>    Revision 1.118  2006/03/14 18:20:07  brouard
 #include <stdio.h>    (Module): varevsij Comments added explaining the second
 #include <stdlib.h>    table of variances if popbased=1 .
 #include <unistd.h>    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 #define MAXLINE 256    (Module): Version 0.98d
 #define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"  
 #define FILENAMELENGTH 80    Revision 1.117  2006/03/14 17:16:22  brouard
 /*#define DEBUG*/    (Module): varevsij Comments added explaining the second
 #define windows    table of variances if popbased=1 .
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    (Module): Function pstamp added
     (Module): Version 0.98d
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
 #define NINTERVMAX 8    varian-covariance of ej. is needed (Saito).
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.115  2006/02/27 12:17:45  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): One freematrix added in mlikeli! 0.98c
 #define MAXN 20000  
 #define YEARM 12. /* Number of months per year */    Revision 1.114  2006/02/26 12:57:58  brouard
 #define AGESUP 130    (Module): Some improvements in processing parameter
 #define AGEBASE 40    filename with strsep.
   
     Revision 1.113  2006/02/24 14:20:24  brouard
 int erreur; /* Error number */    (Module): Memory leaks checks with valgrind and:
 int nvar;    datafile was not closed, some imatrix were not freed and on matrix
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    allocation too.
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.112  2006/01/30 09:55:26  brouard
 int ndeath=1; /* Number of dead states */    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.111  2006/01/25 20:38:18  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): Comments can be added in data file. Missing date values
 int maxwav; /* Maxim number of waves */    can be a simple dot '.'.
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.110  2006/01/25 00:51:50  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): Lots of cleaning and bugs added (Gompertz)
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.109  2006/01/24 19:37:15  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Comments (lines starting with a #) are allowed in data.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    Revision 1.108  2006/01/19 18:05:42  lievre
 FILE *ficgp,*ficresprob,*ficpop;    Gnuplot problem appeared...
 FILE *ficreseij;    To be fixed
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.107  2006/01/19 16:20:37  brouard
   char fileresv[FILENAMELENGTH];    Test existence of gnuplot in imach path
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.106  2006/01/19 13:24:36  brouard
     Some cleaning and links added in html output
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.105  2006/01/05 20:23:19  lievre
 #define FTOL 1.0e-10    *** empty log message ***
   
 #define NRANSI    Revision 1.104  2005/09/30 16:11:43  lievre
 #define ITMAX 200    (Module): sump fixed, loop imx fixed, and simplifications.
     (Module): If the status is missing at the last wave but we know
 #define TOL 2.0e-4    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 #define CGOLD 0.3819660    contributions to the likelihood is 1 - Prob of dying from last
 #define ZEPS 1.0e-10    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    the healthy state at last known wave). Version is 0.98
   
 #define GOLD 1.618034    Revision 1.103  2005/09/30 15:54:49  lievre
 #define GLIMIT 100.0    (Module): sump fixed, loop imx fixed, and simplifications.
 #define TINY 1.0e-20  
     Revision 1.102  2004/09/15 17:31:30  brouard
 static double maxarg1,maxarg2;    Add the possibility to read data file including tab characters.
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.101  2004/09/15 10:38:38  brouard
      Fix on curr_time
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.100  2004/07/12 18:29:06  brouard
     Add version for Mac OS X. Just define UNIX in Makefile
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.99  2004/06/05 08:57:40  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    *** empty log message ***
   
 int imx;    Revision 1.98  2004/05/16 15:05:56  brouard
 int stepm;    New version 0.97 . First attempt to estimate force of mortality
 /* Stepm, step in month: minimum step interpolation*/    directly from the data i.e. without the need of knowing the health
     state at each age, but using a Gompertz model: log u =a + b*age .
 int m,nb;    This is the basic analysis of mortality and should be done before any
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    other analysis, in order to test if the mortality estimated from the
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    cross-longitudinal survey is different from the mortality estimated
 double **pmmij, ***probs, ***mobaverage;    from other sources like vital statistic data.
 double dateintmean=0;  
     The same imach parameter file can be used but the option for mle should be -3.
 double *weight;  
 int **s; /* Status */    Agnès, who wrote this part of the code, tried to keep most of the
 double *agedc, **covar, idx;    former routines in order to include the new code within the former code.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     The output is very simple: only an estimate of the intercept and of
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    the slope with 95% confident intervals.
 double ftolhess; /* Tolerance for computing hessian */  
     Current limitations:
 /**************** split *************************/    A) Even if you enter covariates, i.e. with the
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 {    B) There is no computation of Life Expectancy nor Life Table.
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */    Revision 1.97  2004/02/20 13:25:42  lievre
     Version 0.96d. Population forecasting command line is (temporarily)
    l1 = strlen( path );                 /* length of path */    suppressed.
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  
 #ifdef windows    Revision 1.96  2003/07/15 15:38:55  brouard
    s = strrchr( path, '\\' );           /* find last / */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 #else    rewritten within the same printf. Workaround: many printfs.
    s = strrchr( path, '/' );            /* find last / */  
 #endif    Revision 1.95  2003/07/08 07:54:34  brouard
    if ( s == NULL ) {                   /* no directory, so use current */    * imach.c (Repository):
 #if     defined(__bsd__)                /* get current working directory */    (Repository): Using imachwizard code to output a more meaningful covariance
       extern char       *getwd( );    matrix (cov(a12,c31) instead of numbers.
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.94  2003/06/27 13:00:02  brouard
 #else    Just cleaning
       extern char       *getcwd( );  
     Revision 1.93  2003/06/25 16:33:55  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    (Module): On windows (cygwin) function asctime_r doesn't
 #endif    exist so I changed back to asctime which exists.
          return( GLOCK_ERROR_GETCWD );    (Module): Version 0.96b
       }  
       strcpy( name, path );             /* we've got it */    Revision 1.92  2003/06/25 16:30:45  brouard
    } else {                             /* strip direcotry from path */    (Module): On windows (cygwin) function asctime_r doesn't
       s++;                              /* after this, the filename */    exist so I changed back to asctime which exists.
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.91  2003/06/25 15:30:29  brouard
       strcpy( name, s );                /* save file name */    * imach.c (Repository): Duplicated warning errors corrected.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    (Repository): Elapsed time after each iteration is now output. It
       dirc[l1-l2] = 0;                  /* add zero */    helps to forecast when convergence will be reached. Elapsed time
    }    is stamped in powell.  We created a new html file for the graphs
    l1 = strlen( dirc );                 /* length of directory */    concerning matrix of covariance. It has extension -cov.htm.
 #ifdef windows  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    Revision 1.90  2003/06/24 12:34:15  brouard
 #else    (Module): Some bugs corrected for windows. Also, when
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    mle=-1 a template is output in file "or"mypar.txt with the design
 #endif    of the covariance matrix to be input.
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Revision 1.89  2003/06/24 12:30:52  brouard
    strcpy(ext,s);                       /* save extension */    (Module): Some bugs corrected for windows. Also, when
    l1= strlen( name);    mle=-1 a template is output in file "or"mypar.txt with the design
    l2= strlen( s)+1;    of the covariance matrix to be input.
    strncpy( finame, name, l1-l2);  
    finame[l1-l2]= 0;    Revision 1.88  2003/06/23 17:54:56  brouard
    return( 0 );                         /* we're done */    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 }  
     Revision 1.87  2003/06/18 12:26:01  brouard
     Version 0.96
 /******************************************/  
     Revision 1.86  2003/06/17 20:04:08  brouard
 void replace(char *s, char*t)    (Module): Change position of html and gnuplot routines and added
 {    routine fileappend.
   int i;  
   int lg=20;    Revision 1.85  2003/06/17 13:12:43  brouard
   i=0;    * imach.c (Repository): Check when date of death was earlier that
   lg=strlen(t);    current date of interview. It may happen when the death was just
   for(i=0; i<= lg; i++) {    prior to the death. In this case, dh was negative and likelihood
     (s[i] = t[i]);    was wrong (infinity). We still send an "Error" but patch by
     if (t[i]== '\\') s[i]='/';    assuming that the date of death was just one stepm after the
   }    interview.
 }    (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
 int nbocc(char *s, char occ)    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   int i,j=0;    (Repository): No more line truncation errors.
   int lg=20;  
   i=0;    Revision 1.84  2003/06/13 21:44:43  brouard
   lg=strlen(s);    * imach.c (Repository): Replace "freqsummary" at a correct
   for(i=0; i<= lg; i++) {    place. It differs from routine "prevalence" which may be called
   if  (s[i] == occ ) j++;    many times. Probs is memory consuming and must be used with
   }    parcimony.
   return j;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 }  
     Revision 1.83  2003/06/10 13:39:11  lievre
 void cutv(char *u,char *v, char*t, char occ)    *** empty log message ***
 {  
   int i,lg,j,p=0;    Revision 1.82  2003/06/05 15:57:20  brouard
   i=0;    Add log in  imach.c and  fullversion number is now printed.
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  */
   }  /*
      Interpolated Markov Chain
   lg=strlen(t);  
   for(j=0; j<p; j++) {    Short summary of the programme:
     (u[j] = t[j]);    
   }    This program computes Healthy Life Expectancies from
      u[p]='\0';    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     first survey ("cross") where individuals from different ages are
    for(j=0; j<= lg; j++) {    interviewed on their health status or degree of disability (in the
     if (j>=(p+1))(v[j-p-1] = t[j]);    case of a health survey which is our main interest) -2- at least a
   }    second wave of interviews ("longitudinal") which measure each change
 }    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
 /********************** nrerror ********************/    model. More health states you consider, more time is necessary to reach the
     Maximum Likelihood of the parameters involved in the model.  The
 void nrerror(char error_text[])    simplest model is the multinomial logistic model where pij is the
 {    probability to be observed in state j at the second wave
   fprintf(stderr,"ERREUR ...\n");    conditional to be observed in state i at the first wave. Therefore
   fprintf(stderr,"%s\n",error_text);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   exit(1);    'age' is age and 'sex' is a covariate. If you want to have a more
 }    complex model than "constant and age", you should modify the program
 /*********************** vector *******************/    where the markup *Covariates have to be included here again* invites
 double *vector(int nl, int nh)    you to do it.  More covariates you add, slower the
 {    convergence.
   double *v;  
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    The advantage of this computer programme, compared to a simple
   if (!v) nrerror("allocation failure in vector");    multinomial logistic model, is clear when the delay between waves is not
   return v-nl+NR_END;    identical for each individual. Also, if a individual missed an
 }    intermediate interview, the information is lost, but taken into
     account using an interpolation or extrapolation.  
 /************************ free vector ******************/  
 void free_vector(double*v, int nl, int nh)    hPijx is the probability to be observed in state i at age x+h
 {    conditional to the observed state i at age x. The delay 'h' can be
   free((FREE_ARG)(v+nl-NR_END));    split into an exact number (nh*stepm) of unobserved intermediate
 }    states. This elementary transition (by month, quarter,
     semester or year) is modelled as a multinomial logistic.  The hPx
 /************************ivector *******************************/    matrix is simply the matrix product of nh*stepm elementary matrices
 int *ivector(long nl,long nh)    and the contribution of each individual to the likelihood is simply
 {    hPijx.
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Also this programme outputs the covariance matrix of the parameters but also
   if (!v) nrerror("allocation failure in ivector");    of the life expectancies. It also computes the period (stable) prevalence. 
   return v-nl+NR_END;    
 }    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
              Institut national d'études démographiques, Paris.
 /******************free ivector **************************/    This software have been partly granted by Euro-REVES, a concerted action
 void free_ivector(int *v, long nl, long nh)    from the European Union.
 {    It is copyrighted identically to a GNU software product, ie programme and
   free((FREE_ARG)(v+nl-NR_END));    software can be distributed freely for non commercial use. Latest version
 }    can be accessed at http://euroreves.ined.fr/imach .
   
 /******************* imatrix *******************************/    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 int **imatrix(long nrl, long nrh, long ncl, long nch)    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    
 {    **********************************************************************/
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  /*
   int **m;    main
      read parameterfile
   /* allocate pointers to rows */    read datafile
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    concatwav
   if (!m) nrerror("allocation failure 1 in matrix()");    freqsummary
   m += NR_END;    if (mle >= 1)
   m -= nrl;      mlikeli
      print results files
      if mle==1 
   /* allocate rows and set pointers to them */       computes hessian
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    read end of parameter file: agemin, agemax, bage, fage, estepm
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");        begin-prev-date,...
   m[nrl] += NR_END;    open gnuplot file
   m[nrl] -= ncl;    open html file
      period (stable) prevalence
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;     for age prevalim()
      h Pij x
   /* return pointer to array of pointers to rows */    variance of p varprob
   return m;    forecasting if prevfcast==1 prevforecast call prevalence()
 }    health expectancies
     Variance-covariance of DFLE
 /****************** free_imatrix *************************/    prevalence()
 void free_imatrix(m,nrl,nrh,ncl,nch)     movingaverage()
       int **m;    varevsij() 
       long nch,ncl,nrh,nrl;    if popbased==1 varevsij(,popbased)
      /* free an int matrix allocated by imatrix() */    total life expectancies
 {    Variance of period (stable) prevalence
   free((FREE_ARG) (m[nrl]+ncl-NR_END));   end
   free((FREE_ARG) (m+nrl-NR_END));  */
 }  
   
 /******************* matrix *******************************/  
 double **matrix(long nrl, long nrh, long ncl, long nch)   
 {  #include <math.h>
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  #include <stdio.h>
   double **m;  #include <stdlib.h>
   #include <string.h>
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #include <unistd.h>
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  #include <limits.h>
   m -= nrl;  #include <sys/types.h>
   #include <sys/stat.h>
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #include <errno.h>
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  extern int errno;
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /* #include <sys/time.h> */
   #include <time.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include "timeval.h"
   return m;  
 }  /* #include <libintl.h> */
   /* #define _(String) gettext (String) */
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #define MAXLINE 256
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define GNUPLOTPROGRAM "gnuplot"
   free((FREE_ARG)(m+nrl-NR_END));  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 }  #define FILENAMELENGTH 132
   
 /******************* ma3x *******************************/  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   double ***m;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define NINTERVMAX 8
   if (!m) nrerror("allocation failure 1 in matrix()");  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   m += NR_END;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   m -= nrl;  #define NCOVMAX 8 /* Maximum number of covariates */
   #define MAXN 20000
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define YEARM 12. /* Number of months per year */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define AGESUP 130
   m[nrl] += NR_END;  #define AGEBASE 40
   m[nrl] -= ncl;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   #ifdef UNIX
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define DIRSEPARATOR '/'
   #define CHARSEPARATOR "/"
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #define ODIRSEPARATOR '\\'
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #else
   m[nrl][ncl] += NR_END;  #define DIRSEPARATOR '\\'
   m[nrl][ncl] -= nll;  #define CHARSEPARATOR "\\"
   for (j=ncl+1; j<=nch; j++)  #define ODIRSEPARATOR '/'
     m[nrl][j]=m[nrl][j-1]+nlay;  #endif
    
   for (i=nrl+1; i<=nrh; i++) {  /* $Id$ */
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  /* $State$ */
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;  char version[]="Imach version 0.98h, April 2006, INED-EUROREVES-Institut de longevite ";
   }  char fullversion[]="$Revision$ $Date$"; 
   return m;  char strstart[80];
 }  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 /*************************free ma3x ************************/  int nvar;
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
 {  int npar=NPARMAX;
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  int nlstate=2; /* Number of live states */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  int ndeath=1; /* Number of dead states */
   free((FREE_ARG)(m+nrl-NR_END));  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 }  int popbased=0;
   
 /***************** f1dim *************************/  int *wav; /* Number of waves for this individuual 0 is possible */
 extern int ncom;  int maxwav; /* Maxim number of waves */
 extern double *pcom,*xicom;  int jmin, jmax; /* min, max spacing between 2 waves */
 extern double (*nrfunc)(double []);  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
    int gipmx, gsw; /* Global variables on the number of contributions 
 double f1dim(double x)                     to the likelihood and the sum of weights (done by funcone)*/
 {  int mle, weightopt;
   int j;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   double f;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   double *xt;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
               * wave mi and wave mi+1 is not an exact multiple of stepm. */
   xt=vector(1,ncom);  double jmean; /* Mean space between 2 waves */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  double **oldm, **newm, **savm; /* Working pointers to matrices */
   f=(*nrfunc)(xt);  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   free_vector(xt,1,ncom);  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   return f;  FILE *ficlog, *ficrespow;
 }  int globpr; /* Global variable for printing or not */
   double fretone; /* Only one call to likelihood */
 /*****************brent *************************/  long ipmx; /* Number of contributions */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  double sw; /* Sum of weights */
 {  char filerespow[FILENAMELENGTH];
   int iter;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   double a,b,d,etemp;  FILE *ficresilk;
   double fu,fv,fw,fx;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   double ftemp;  FILE *ficresprobmorprev;
   double p,q,r,tol1,tol2,u,v,w,x,xm;  FILE *fichtm, *fichtmcov; /* Html File */
   double e=0.0;  FILE *ficreseij;
    char filerese[FILENAMELENGTH];
   a=(ax < cx ? ax : cx);  FILE *ficresstdeij;
   b=(ax > cx ? ax : cx);  char fileresstde[FILENAMELENGTH];
   x=w=v=bx;  FILE *ficrescveij;
   fw=fv=fx=(*f)(x);  char filerescve[FILENAMELENGTH];
   for (iter=1;iter<=ITMAX;iter++) {  FILE  *ficresvij;
     xm=0.5*(a+b);  char fileresv[FILENAMELENGTH];
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  FILE  *ficresvpl;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  char fileresvpl[FILENAMELENGTH];
     printf(".");fflush(stdout);  char title[MAXLINE];
 #ifdef DEBUG  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
 #endif  char command[FILENAMELENGTH];
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int  outcmd=0;
       *xmin=x;  
       return fx;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     }  
     ftemp=fu;  char filelog[FILENAMELENGTH]; /* Log file */
     if (fabs(e) > tol1) {  char filerest[FILENAMELENGTH];
       r=(x-w)*(fx-fv);  char fileregp[FILENAMELENGTH];
       q=(x-v)*(fx-fw);  char popfile[FILENAMELENGTH];
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       if (q > 0.0) p = -p;  
       q=fabs(q);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
       etemp=e;  struct timezone tzp;
       e=d;  extern int gettimeofday();
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  struct tm tmg, tm, tmf, *gmtime(), *localtime();
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  long time_value;
       else {  extern long time();
         d=p/q;  char strcurr[80], strfor[80];
         u=x+d;  
         if (u-a < tol2 || b-u < tol2)  char *endptr;
           d=SIGN(tol1,xm-x);  long lval;
       }  double dval;
     } else {  
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define NR_END 1
     }  #define FREE_ARG char*
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  #define FTOL 1.0e-10
     fu=(*f)(u);  
     if (fu <= fx) {  #define NRANSI 
       if (u >= x) a=x; else b=x;  #define ITMAX 200 
       SHFT(v,w,x,u)  
         SHFT(fv,fw,fx,fu)  #define TOL 2.0e-4 
         } else {  
           if (u < x) a=u; else b=u;  #define CGOLD 0.3819660 
           if (fu <= fw || w == x) {  #define ZEPS 1.0e-10 
             v=w;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
             w=u;  
             fv=fw;  #define GOLD 1.618034 
             fw=fu;  #define GLIMIT 100.0 
           } else if (fu <= fv || v == x || v == w) {  #define TINY 1.0e-20 
             v=u;  
             fv=fu;  static double maxarg1,maxarg2;
           }  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
         }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   }    
   nrerror("Too many iterations in brent");  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   *xmin=x;  #define rint(a) floor(a+0.5)
   return fx;  
 }  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 /****************** mnbrak ***********************/  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int agegomp= AGEGOMP;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  int imx; 
 {  int stepm=1;
   double ulim,u,r,q, dum;  /* Stepm, step in month: minimum step interpolation*/
   double fu;  
    int estepm;
   *fa=(*func)(*ax);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  int m,nb;
     SHFT(dum,*ax,*bx,dum)  long *num;
       SHFT(dum,*fb,*fa,dum)  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
       }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   *cx=(*bx)+GOLD*(*bx-*ax);  double **pmmij, ***probs;
   *fc=(*func)(*cx);  double *ageexmed,*agecens;
   while (*fb > *fc) {  double dateintmean=0;
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  double *weight;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  int **s; /* Status */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  double *agedc, **covar, idx;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
     if ((*bx-u)*(u-*cx) > 0.0) {  double *lsurv, *lpop, *tpop;
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
       fu=(*func)(u);  double ftolhess; /* Tolerance for computing hessian */
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  /**************** split *************************/
           SHFT(*fb,*fc,fu,(*func)(u))  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
           }  {
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       u=ulim;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       fu=(*func)(u);    */ 
     } else {    char  *ss;                            /* pointer */
       u=(*cx)+GOLD*(*cx-*bx);    int   l1, l2;                         /* length counters */
       fu=(*func)(u);  
     }    l1 = strlen(path );                   /* length of path */
     SHFT(*ax,*bx,*cx,u)    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       SHFT(*fa,*fb,*fc,fu)    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       }    if ( ss == NULL ) {                   /* no directory, so determine current directory */
 }      strcpy( name, path );               /* we got the fullname name because no directory */
       /*if(strrchr(path, ODIRSEPARATOR )==NULL)
 /*************** linmin ************************/        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       /* get current working directory */
 int ncom;      /*    extern  char* getcwd ( char *buf , int len);*/
 double *pcom,*xicom;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 double (*nrfunc)(double []);        return( GLOCK_ERROR_GETCWD );
        }
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))      /* got dirc from getcwd*/
 {      printf(" DIRC = %s \n",dirc);
   double brent(double ax, double bx, double cx,    } else {                              /* strip direcotry from path */
                double (*f)(double), double tol, double *xmin);      ss++;                               /* after this, the filename */
   double f1dim(double x);      l2 = strlen( ss );                  /* length of filename */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
               double *fc, double (*func)(double));      strcpy( name, ss );         /* save file name */
   int j;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   double xx,xmin,bx,ax;      dirc[l1-l2] = 0;                    /* add zero */
   double fx,fb,fa;      printf(" DIRC2 = %s \n",dirc);
      }
   ncom=n;    /* We add a separator at the end of dirc if not exists */
   pcom=vector(1,n);    l1 = strlen( dirc );                  /* length of directory */
   xicom=vector(1,n);    if( dirc[l1-1] != DIRSEPARATOR ){
   nrfunc=func;      dirc[l1] =  DIRSEPARATOR;
   for (j=1;j<=n;j++) {      dirc[l1+1] = 0; 
     pcom[j]=p[j];      printf(" DIRC3 = %s \n",dirc);
     xicom[j]=xi[j];    }
   }    ss = strrchr( name, '.' );            /* find last / */
   ax=0.0;    if (ss >0){
   xx=1.0;      ss++;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);      strcpy(ext,ss);                     /* save extension */
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);      l1= strlen( name);
 #ifdef DEBUG      l2= strlen(ss)+1;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);      strncpy( finame, name, l1-l2);
 #endif      finame[l1-l2]= 0;
   for (j=1;j<=n;j++) {    }
     xi[j] *= xmin;  
     p[j] += xi[j];    return( 0 );                          /* we're done */
   }  }
   free_vector(xicom,1,n);  
   free_vector(pcom,1,n);  
 }  /******************************************/
   
 /*************** powell ************************/  void replace_back_to_slash(char *s, char*t)
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  {
             double (*func)(double []))    int i;
 {    int lg=0;
   void linmin(double p[], double xi[], int n, double *fret,    i=0;
               double (*func)(double []));    lg=strlen(t);
   int i,ibig,j;    for(i=0; i<= lg; i++) {
   double del,t,*pt,*ptt,*xit;      (s[i] = t[i]);
   double fp,fptt;      if (t[i]== '\\') s[i]='/';
   double *xits;    }
   pt=vector(1,n);  }
   ptt=vector(1,n);  
   xit=vector(1,n);  int nbocc(char *s, char occ)
   xits=vector(1,n);  {
   *fret=(*func)(p);    int i,j=0;
   for (j=1;j<=n;j++) pt[j]=p[j];    int lg=20;
   for (*iter=1;;++(*iter)) {    i=0;
     fp=(*fret);    lg=strlen(s);
     ibig=0;    for(i=0; i<= lg; i++) {
     del=0.0;    if  (s[i] == occ ) j++;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    }
     for (i=1;i<=n;i++)    return j;
       printf(" %d %.12f",i, p[i]);  }
     printf("\n");  
     for (i=1;i<=n;i++) {  void cutv(char *u,char *v, char*t, char occ)
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  {
       fptt=(*fret);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
 #ifdef DEBUG       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       printf("fret=%lf \n",*fret);       gives u="abcedf" and v="ghi2j" */
 #endif    int i,lg,j,p=0;
       printf("%d",i);fflush(stdout);    i=0;
       linmin(p,xit,n,fret,func);    for(j=0; j<=strlen(t)-1; j++) {
       if (fabs(fptt-(*fret)) > del) {      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
         del=fabs(fptt-(*fret));    }
         ibig=i;  
       }    lg=strlen(t);
 #ifdef DEBUG    for(j=0; j<p; j++) {
       printf("%d %.12e",i,(*fret));      (u[j] = t[j]);
       for (j=1;j<=n;j++) {    }
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);       u[p]='\0';
         printf(" x(%d)=%.12e",j,xit[j]);  
       }     for(j=0; j<= lg; j++) {
       for(j=1;j<=n;j++)      if (j>=(p+1))(v[j-p-1] = t[j]);
         printf(" p=%.12e",p[j]);    }
       printf("\n");  }
 #endif  
     }  /********************** nrerror ********************/
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG  void nrerror(char error_text[])
       int k[2],l;  {
       k[0]=1;    fprintf(stderr,"ERREUR ...\n");
       k[1]=-1;    fprintf(stderr,"%s\n",error_text);
       printf("Max: %.12e",(*func)(p));    exit(EXIT_FAILURE);
       for (j=1;j<=n;j++)  }
         printf(" %.12e",p[j]);  /*********************** vector *******************/
       printf("\n");  double *vector(int nl, int nh)
       for(l=0;l<=1;l++) {  {
         for (j=1;j<=n;j++) {    double *v;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    if (!v) nrerror("allocation failure in vector");
         }    return v-nl+NR_END;
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  }
       }  
 #endif  /************************ free vector ******************/
   void free_vector(double*v, int nl, int nh)
   {
       free_vector(xit,1,n);    free((FREE_ARG)(v+nl-NR_END));
       free_vector(xits,1,n);  }
       free_vector(ptt,1,n);  
       free_vector(pt,1,n);  /************************ivector *******************************/
       return;  int *ivector(long nl,long nh)
     }  {
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    int *v;
     for (j=1;j<=n;j++) {    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       ptt[j]=2.0*p[j]-pt[j];    if (!v) nrerror("allocation failure in ivector");
       xit[j]=p[j]-pt[j];    return v-nl+NR_END;
       pt[j]=p[j];  }
     }  
     fptt=(*func)(ptt);  /******************free ivector **************************/
     if (fptt < fp) {  void free_ivector(int *v, long nl, long nh)
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  {
       if (t < 0.0) {    free((FREE_ARG)(v+nl-NR_END));
         linmin(p,xit,n,fret,func);  }
         for (j=1;j<=n;j++) {  
           xi[j][ibig]=xi[j][n];  /************************lvector *******************************/
           xi[j][n]=xit[j];  long *lvector(long nl,long nh)
         }  {
 #ifdef DEBUG    long *v;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
         for(j=1;j<=n;j++)    if (!v) nrerror("allocation failure in ivector");
           printf(" %.12e",xit[j]);    return v-nl+NR_END;
         printf("\n");  }
 #endif  
       }  /******************free lvector **************************/
     }  void free_lvector(long *v, long nl, long nh)
   }  {
 }    free((FREE_ARG)(v+nl-NR_END));
   }
 /**** Prevalence limit ****************/  
   /******************* imatrix *******************************/
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  int **imatrix(long nrl, long nrh, long ncl, long nch) 
 {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  { 
      matrix by transitions matrix until convergence is reached */    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     int **m; 
   int i, ii,j,k;    
   double min, max, maxmin, maxmax,sumnew=0.;    /* allocate pointers to rows */ 
   double **matprod2();    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   double **out, cov[NCOVMAX], **pmij();    if (!m) nrerror("allocation failure 1 in matrix()"); 
   double **newm;    m += NR_END; 
   double agefin, delaymax=50 ; /* Max number of years to converge */    m -= nrl; 
     
   for (ii=1;ii<=nlstate+ndeath;ii++)    
     for (j=1;j<=nlstate+ndeath;j++){    /* allocate rows and set pointers to them */ 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     m[nrl] += NR_END; 
    cov[1]=1.;    m[nrl] -= ncl; 
      
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    
     newm=savm;    /* return pointer to array of pointers to rows */ 
     /* Covariates have to be included here again */    return m; 
      cov[2]=agefin;  } 
    
       for (k=1; k<=cptcovn;k++) {  /****************** free_imatrix *************************/
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  void free_imatrix(m,nrl,nrh,ncl,nch)
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/        int **m;
       }        long nch,ncl,nrh,nrl; 
       for (k=1; k<=cptcovage;k++)       /* free an int matrix allocated by imatrix() */ 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  { 
       for (k=1; k<=cptcovprod;k++)    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    free((FREE_ARG) (m+nrl-NR_END)); 
   } 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /******************* matrix *******************************/
   double **matrix(long nrl, long nrh, long ncl, long nch)
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     savm=oldm;    double **m;
     oldm=newm;  
     maxmax=0.;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     for(j=1;j<=nlstate;j++){    if (!m) nrerror("allocation failure 1 in matrix()");
       min=1.;    m += NR_END;
       max=0.;    m -= nrl;
       for(i=1; i<=nlstate; i++) {  
         sumnew=0;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         prlim[i][j]= newm[i][j]/(1-sumnew);    m[nrl] += NR_END;
         max=FMAX(max,prlim[i][j]);    m[nrl] -= ncl;
         min=FMIN(min,prlim[i][j]);  
       }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       maxmin=max-min;    return m;
       maxmax=FMAX(maxmax,maxmin);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
     }     */
     if(maxmax < ftolpl){  }
       return prlim;  
     }  /*************************free matrix ************************/
   }  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
 }  {
     free((FREE_ARG)(m[nrl]+ncl-NR_END));
 /*************** transition probabilities ***************/    free((FREE_ARG)(m+nrl-NR_END));
   }
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  
 {  /******************* ma3x *******************************/
   double s1, s2;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   /*double t34;*/  {
   int i,j,j1, nc, ii, jj;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     double ***m;
     for(i=1; i<= nlstate; i++){  
     for(j=1; j<i;j++){    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    if (!m) nrerror("allocation failure 1 in matrix()");
         /*s2 += param[i][j][nc]*cov[nc];*/    m += NR_END;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    m -= nrl;
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  
       }    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       ps[i][j]=s2;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    m[nrl] += NR_END;
     }    m[nrl] -= ncl;
     for(j=i+1; j<=nlstate+ndeath;j++){  
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       }    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       ps[i][j]=s2;    m[nrl][ncl] += NR_END;
     }    m[nrl][ncl] -= nll;
   }    for (j=ncl+1; j<=nch; j++) 
     /*ps[3][2]=1;*/      m[nrl][j]=m[nrl][j-1]+nlay;
     
   for(i=1; i<= nlstate; i++){    for (i=nrl+1; i<=nrh; i++) {
      s1=0;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     for(j=1; j<i; j++)      for (j=ncl+1; j<=nch; j++) 
       s1+=exp(ps[i][j]);        m[i][j]=m[i][j-1]+nlay;
     for(j=i+1; j<=nlstate+ndeath; j++)    }
       s1+=exp(ps[i][j]);    return m; 
     ps[i][i]=1./(s1+1.);    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     for(j=1; j<i; j++)             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       ps[i][j]= exp(ps[i][j])*ps[i][i];    */
     for(j=i+1; j<=nlstate+ndeath; j++)  }
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  /*************************free ma3x ************************/
   } /* end i */  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   {
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     for(jj=1; jj<= nlstate+ndeath; jj++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       ps[ii][jj]=0;    free((FREE_ARG)(m+nrl-NR_END));
       ps[ii][ii]=1;  }
     }  
   }  /*************** function subdirf ***********/
   char *subdirf(char fileres[])
   {
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    /* Caution optionfilefiname is hidden */
     for(jj=1; jj<= nlstate+ndeath; jj++){    strcpy(tmpout,optionfilefiname);
      printf("%lf ",ps[ii][jj]);    strcat(tmpout,"/"); /* Add to the right */
    }    strcat(tmpout,fileres);
     printf("\n ");    return tmpout;
     }  }
     printf("\n ");printf("%lf ",cov[2]);*/  
 /*  /*************** function subdirf2 ***********/
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  char *subdirf2(char fileres[], char *preop)
   goto end;*/  {
     return ps;    
 }    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
 /**************** Product of 2 matrices ******************/    strcat(tmpout,"/");
     strcat(tmpout,preop);
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    strcat(tmpout,fileres);
 {    return tmpout;
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  }
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  
   /* in, b, out are matrice of pointers which should have been initialized  /*************** function subdirf3 ***********/
      before: only the contents of out is modified. The function returns  char *subdirf3(char fileres[], char *preop, char *preop2)
      a pointer to pointers identical to out */  {
   long i, j, k;    
   for(i=nrl; i<= nrh; i++)    /* Caution optionfilefiname is hidden */
     for(k=ncolol; k<=ncoloh; k++)    strcpy(tmpout,optionfilefiname);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    strcat(tmpout,"/");
         out[i][k] +=in[i][j]*b[j][k];    strcat(tmpout,preop);
     strcat(tmpout,preop2);
   return out;    strcat(tmpout,fileres);
 }    return tmpout;
   }
   
 /************* Higher Matrix Product ***************/  /***************** f1dim *************************/
   extern int ncom; 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  extern double *pcom,*xicom;
 {  extern double (*nrfunc)(double []); 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month   
      duration (i.e. until  double f1dim(double x) 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  { 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    int j; 
      (typically every 2 years instead of every month which is too big).    double f;
      Model is determined by parameters x and covariates have to be    double *xt; 
      included manually here.   
     xt=vector(1,ncom); 
      */    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
   int i, j, d, h, k;    free_vector(xt,1,ncom); 
   double **out, cov[NCOVMAX];    return f; 
   double **newm;  } 
   
   /* Hstepm could be zero and should return the unit matrix */  /*****************brent *************************/
   for (i=1;i<=nlstate+ndeath;i++)  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     for (j=1;j<=nlstate+ndeath;j++){  { 
       oldm[i][j]=(i==j ? 1.0 : 0.0);    int iter; 
       po[i][j][0]=(i==j ? 1.0 : 0.0);    double a,b,d,etemp;
     }    double fu,fv,fw,fx;
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    double ftemp;
   for(h=1; h <=nhstepm; h++){    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     for(d=1; d <=hstepm; d++){    double e=0.0; 
       newm=savm;   
       /* Covariates have to be included here again */    a=(ax < cx ? ax : cx); 
       cov[1]=1.;    b=(ax > cx ? ax : cx); 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    x=w=v=bx; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    fw=fv=fx=(*f)(x); 
       for (k=1; k<=cptcovage;k++)    for (iter=1;iter<=ITMAX;iter++) { 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      xm=0.5*(a+b); 
       for (k=1; k<=cptcovprod;k++)      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       printf(".");fflush(stdout);
       fprintf(ficlog,".");fflush(ficlog);
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  #ifdef DEBUG
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
       savm=oldm;  #endif
       oldm=newm;      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     }        *xmin=x; 
     for(i=1; i<=nlstate+ndeath; i++)        return fx; 
       for(j=1;j<=nlstate+ndeath;j++) {      } 
         po[i][j][h]=newm[i][j];      ftemp=fu;
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      if (fabs(e) > tol1) { 
          */        r=(x-w)*(fx-fv); 
       }        q=(x-v)*(fx-fw); 
   } /* end h */        p=(x-v)*q-(x-w)*r; 
   return po;        q=2.0*(q-r); 
 }        if (q > 0.0) p = -p; 
         q=fabs(q); 
         etemp=e; 
 /*************** log-likelihood *************/        e=d; 
 double func( double *x)        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
 {          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   int i, ii, j, k, mi, d, kk;        else { 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];          d=p/q; 
   double **out;          u=x+d; 
   double sw; /* Sum of weights */          if (u-a < tol2 || b-u < tol2) 
   double lli; /* Individual log likelihood */            d=SIGN(tol1,xm-x); 
   long ipmx;        } 
   /*extern weight */      } else { 
   /* We are differentiating ll according to initial status */        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      } 
   /*for(i=1;i<imx;i++)      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     printf(" %d\n",s[4][i]);      fu=(*f)(u); 
   */      if (fu <= fx) { 
   cov[1]=1.;        if (u >= x) a=x; else b=x; 
         SHFT(v,w,x,u) 
   for(k=1; k<=nlstate; k++) ll[k]=0.;          SHFT(fv,fw,fx,fu) 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){          } else { 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];            if (u < x) a=u; else b=u; 
     for(mi=1; mi<= wav[i]-1; mi++){            if (fu <= fw || w == x) { 
       for (ii=1;ii<=nlstate+ndeath;ii++)              v=w; 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);              w=u; 
       for(d=0; d<dh[mi][i]; d++){              fv=fw; 
         newm=savm;              fw=fu; 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;            } else if (fu <= fv || v == x || v == w) { 
         for (kk=1; kk<=cptcovage;kk++) {              v=u; 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];              fv=fu; 
         }            } 
                  } 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    } 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    nrerror("Too many iterations in brent"); 
         savm=oldm;    *xmin=x; 
         oldm=newm;    return fx; 
          } 
          
       } /* end mult */  /****************** mnbrak ***********************/
        
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/              double (*func)(double)) 
       ipmx +=1;  { 
       sw += weight[i];    double ulim,u,r,q, dum;
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    double fu; 
     } /* end of wave */   
   } /* end of individual */    *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    if (*fb > *fa) { 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      SHFT(dum,*ax,*bx,dum) 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */        SHFT(dum,*fb,*fa,dum) 
   return -l;        } 
 }    *cx=(*bx)+GOLD*(*bx-*ax); 
     *fc=(*func)(*cx); 
     while (*fb > *fc) { 
 /*********** Maximum Likelihood Estimation ***************/      r=(*bx-*ax)*(*fb-*fc); 
       q=(*bx-*cx)*(*fb-*fa); 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
 {        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   int i,j, iter;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
   double **xi,*delti;      if ((*bx-u)*(u-*cx) > 0.0) { 
   double fret;        fu=(*func)(u); 
   xi=matrix(1,npar,1,npar);      } else if ((*cx-u)*(u-ulim) > 0.0) { 
   for (i=1;i<=npar;i++)        fu=(*func)(u); 
     for (j=1;j<=npar;j++)        if (fu < *fc) { 
       xi[i][j]=(i==j ? 1.0 : 0.0);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   printf("Powell\n");            SHFT(*fb,*fc,fu,(*func)(u)) 
   powell(p,xi,npar,ftol,&iter,&fret,func);            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));        u=ulim; 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));        fu=(*func)(u); 
       } else { 
 }        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
 /**** Computes Hessian and covariance matrix ***/      } 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      SHFT(*ax,*bx,*cx,u) 
 {        SHFT(*fa,*fb,*fc,fu) 
   double  **a,**y,*x,pd;        } 
   double **hess;  } 
   int i, j,jk;  
   int *indx;  /*************** linmin ************************/
   
   double hessii(double p[], double delta, int theta, double delti[]);  int ncom; 
   double hessij(double p[], double delti[], int i, int j);  double *pcom,*xicom;
   void lubksb(double **a, int npar, int *indx, double b[]) ;  double (*nrfunc)(double []); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;   
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   hess=matrix(1,npar,1,npar);  { 
     double brent(double ax, double bx, double cx, 
   printf("\nCalculation of the hessian matrix. Wait...\n");                 double (*f)(double), double tol, double *xmin); 
   for (i=1;i<=npar;i++){    double f1dim(double x); 
     printf("%d",i);fflush(stdout);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     hess[i][i]=hessii(p,ftolhess,i,delti);                double *fc, double (*func)(double)); 
     /*printf(" %f ",p[i]);*/    int j; 
     /*printf(" %lf ",hess[i][i]);*/    double xx,xmin,bx,ax; 
   }    double fx,fb,fa;
     
   for (i=1;i<=npar;i++) {    ncom=n; 
     for (j=1;j<=npar;j++)  {    pcom=vector(1,n); 
       if (j>i) {    xicom=vector(1,n); 
         printf(".%d%d",i,j);fflush(stdout);    nrfunc=func; 
         hess[i][j]=hessij(p,delti,i,j);    for (j=1;j<=n;j++) { 
         hess[j][i]=hess[i][j];          pcom[j]=p[j]; 
         /*printf(" %lf ",hess[i][j]);*/      xicom[j]=xi[j]; 
       }    } 
     }    ax=0.0; 
   }    xx=1.0; 
   printf("\n");    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  #ifdef DEBUG
      printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   a=matrix(1,npar,1,npar);    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   y=matrix(1,npar,1,npar);  #endif
   x=vector(1,npar);    for (j=1;j<=n;j++) { 
   indx=ivector(1,npar);      xi[j] *= xmin; 
   for (i=1;i<=npar;i++)      p[j] += xi[j]; 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    } 
   ludcmp(a,npar,indx,&pd);    free_vector(xicom,1,n); 
     free_vector(pcom,1,n); 
   for (j=1;j<=npar;j++) {  } 
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;  char *asc_diff_time(long time_sec, char ascdiff[])
     lubksb(a,npar,indx,x);  {
     for (i=1;i<=npar;i++){    long sec_left, days, hours, minutes;
       matcov[i][j]=x[i];    days = (time_sec) / (60*60*24);
     }    sec_left = (time_sec) % (60*60*24);
   }    hours = (sec_left) / (60*60) ;
     sec_left = (sec_left) %(60*60);
   printf("\n#Hessian matrix#\n");    minutes = (sec_left) /60;
   for (i=1;i<=npar;i++) {    sec_left = (sec_left) % (60);
     for (j=1;j<=npar;j++) {    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
       printf("%.3e ",hess[i][j]);    return ascdiff;
     }  }
     printf("\n");  
   }  /*************** powell ************************/
   void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   /* Recompute Inverse */              double (*func)(double [])) 
   for (i=1;i<=npar;i++)  { 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    void linmin(double p[], double xi[], int n, double *fret, 
   ludcmp(a,npar,indx,&pd);                double (*func)(double [])); 
     int i,ibig,j; 
   /*  printf("\n#Hessian matrix recomputed#\n");    double del,t,*pt,*ptt,*xit;
     double fp,fptt;
   for (j=1;j<=npar;j++) {    double *xits;
     for (i=1;i<=npar;i++) x[i]=0;    int niterf, itmp;
     x[j]=1;  
     lubksb(a,npar,indx,x);    pt=vector(1,n); 
     for (i=1;i<=npar;i++){    ptt=vector(1,n); 
       y[i][j]=x[i];    xit=vector(1,n); 
       printf("%.3e ",y[i][j]);    xits=vector(1,n); 
     }    *fret=(*func)(p); 
     printf("\n");    for (j=1;j<=n;j++) pt[j]=p[j]; 
   }    for (*iter=1;;++(*iter)) { 
   */      fp=(*fret); 
       ibig=0; 
   free_matrix(a,1,npar,1,npar);      del=0.0; 
   free_matrix(y,1,npar,1,npar);      last_time=curr_time;
   free_vector(x,1,npar);      (void) gettimeofday(&curr_time,&tzp);
   free_ivector(indx,1,npar);      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
   free_matrix(hess,1,npar,1,npar);      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
   /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
      for (i=1;i<=n;i++) {
 }        printf(" %d %.12f",i, p[i]);
         fprintf(ficlog," %d %.12lf",i, p[i]);
 /*************** hessian matrix ****************/        fprintf(ficrespow," %.12lf", p[i]);
 double hessii( double x[], double delta, int theta, double delti[])      }
 {      printf("\n");
   int i;      fprintf(ficlog,"\n");
   int l=1, lmax=20;      fprintf(ficrespow,"\n");fflush(ficrespow);
   double k1,k2;      if(*iter <=3){
   double p2[NPARMAX+1];        tm = *localtime(&curr_time.tv_sec);
   double res;        strcpy(strcurr,asctime(&tm));
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  /*       asctime_r(&tm,strcurr); */
   double fx;        forecast_time=curr_time; 
   int k=0,kmax=10;        itmp = strlen(strcurr);
   double l1;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
           strcurr[itmp-1]='\0';
   fx=func(x);        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   for (i=1;i<=npar;i++) p2[i]=x[i];        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   for(l=0 ; l <=lmax; l++){        for(niterf=10;niterf<=30;niterf+=10){
     l1=pow(10,l);          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     delts=delt;          tmf = *localtime(&forecast_time.tv_sec);
     for(k=1 ; k <kmax; k=k+1){  /*      asctime_r(&tmf,strfor); */
       delt = delta*(l1*k);          strcpy(strfor,asctime(&tmf));
       p2[theta]=x[theta] +delt;          itmp = strlen(strfor);
       k1=func(p2)-fx;          if(strfor[itmp-1]=='\n')
       p2[theta]=x[theta]-delt;          strfor[itmp-1]='\0';
       k2=func(p2)-fx;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
       /*res= (k1-2.0*fx+k2)/delt/delt; */          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        }
            }
 #ifdef DEBUG      for (i=1;i<=n;i++) { 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 #endif        fptt=(*fret); 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  #ifdef DEBUG
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        printf("fret=%lf \n",*fret);
         k=kmax;        fprintf(ficlog,"fret=%lf \n",*fret);
       }  #endif
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        printf("%d",i);fflush(stdout);
         k=kmax; l=lmax*10.;        fprintf(ficlog,"%d",i);fflush(ficlog);
       }        linmin(p,xit,n,fret,func); 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        if (fabs(fptt-(*fret)) > del) { 
         delts=delt;          del=fabs(fptt-(*fret)); 
       }          ibig=i; 
     }        } 
   }  #ifdef DEBUG
   delti[theta]=delts;        printf("%d %.12e",i,(*fret));
   return res;        fprintf(ficlog,"%d %.12e",i,(*fret));
          for (j=1;j<=n;j++) {
 }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           printf(" x(%d)=%.12e",j,xit[j]);
 double hessij( double x[], double delti[], int thetai,int thetaj)          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
 {        }
   int i;        for(j=1;j<=n;j++) {
   int l=1, l1, lmax=20;          printf(" p=%.12e",p[j]);
   double k1,k2,k3,k4,res,fx;          fprintf(ficlog," p=%.12e",p[j]);
   double p2[NPARMAX+1];        }
   int k;        printf("\n");
         fprintf(ficlog,"\n");
   fx=func(x);  #endif
   for (k=1; k<=2; k++) {      } 
     for (i=1;i<=npar;i++) p2[i]=x[i];      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     p2[thetai]=x[thetai]+delti[thetai]/k;  #ifdef DEBUG
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        int k[2],l;
     k1=func(p2)-fx;        k[0]=1;
          k[1]=-1;
     p2[thetai]=x[thetai]+delti[thetai]/k;        printf("Max: %.12e",(*func)(p));
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        fprintf(ficlog,"Max: %.12e",(*func)(p));
     k2=func(p2)-fx;        for (j=1;j<=n;j++) {
            printf(" %.12e",p[j]);
     p2[thetai]=x[thetai]-delti[thetai]/k;          fprintf(ficlog," %.12e",p[j]);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        }
     k3=func(p2)-fx;        printf("\n");
          fprintf(ficlog,"\n");
     p2[thetai]=x[thetai]-delti[thetai]/k;        for(l=0;l<=1;l++) {
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          for (j=1;j<=n;j++) {
     k4=func(p2)-fx;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
 #ifdef DEBUG            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);          }
 #endif          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   }          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   return res;        }
 }  #endif
   
 /************** Inverse of matrix **************/  
 void ludcmp(double **a, int n, int *indx, double *d)        free_vector(xit,1,n); 
 {        free_vector(xits,1,n); 
   int i,imax,j,k;        free_vector(ptt,1,n); 
   double big,dum,sum,temp;        free_vector(pt,1,n); 
   double *vv;        return; 
        } 
   vv=vector(1,n);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   *d=1.0;      for (j=1;j<=n;j++) { 
   for (i=1;i<=n;i++) {        ptt[j]=2.0*p[j]-pt[j]; 
     big=0.0;        xit[j]=p[j]-pt[j]; 
     for (j=1;j<=n;j++)        pt[j]=p[j]; 
       if ((temp=fabs(a[i][j])) > big) big=temp;      } 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");      fptt=(*func)(ptt); 
     vv[i]=1.0/big;      if (fptt < fp) { 
   }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
   for (j=1;j<=n;j++) {        if (t < 0.0) { 
     for (i=1;i<j;i++) {          linmin(p,xit,n,fret,func); 
       sum=a[i][j];          for (j=1;j<=n;j++) { 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];            xi[j][ibig]=xi[j][n]; 
       a[i][j]=sum;            xi[j][n]=xit[j]; 
     }          }
     big=0.0;  #ifdef DEBUG
     for (i=j;i<=n;i++) {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       sum=a[i][j];          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       for (k=1;k<j;k++)          for(j=1;j<=n;j++){
         sum -= a[i][k]*a[k][j];            printf(" %.12e",xit[j]);
       a[i][j]=sum;            fprintf(ficlog," %.12e",xit[j]);
       if ( (dum=vv[i]*fabs(sum)) >= big) {          }
         big=dum;          printf("\n");
         imax=i;          fprintf(ficlog,"\n");
       }  #endif
     }        }
     if (j != imax) {      } 
       for (k=1;k<=n;k++) {    } 
         dum=a[imax][k];  } 
         a[imax][k]=a[j][k];  
         a[j][k]=dum;  /**** Prevalence limit (stable or period prevalence)  ****************/
       }  
       *d = -(*d);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       vv[imax]=vv[j];  {
     }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     indx[j]=imax;       matrix by transitions matrix until convergence is reached */
     if (a[j][j] == 0.0) a[j][j]=TINY;  
     if (j != n) {    int i, ii,j,k;
       dum=1.0/(a[j][j]);    double min, max, maxmin, maxmax,sumnew=0.;
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    double **matprod2();
     }    double **out, cov[NCOVMAX], **pmij();
   }    double **newm;
   free_vector(vv,1,n);  /* Doesn't work */    double agefin, delaymax=50 ; /* Max number of years to converge */
 ;  
 }    for (ii=1;ii<=nlstate+ndeath;ii++)
       for (j=1;j<=nlstate+ndeath;j++){
 void lubksb(double **a, int n, int *indx, double b[])        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 {      }
   int i,ii=0,ip,j;  
   double sum;     cov[1]=1.;
     
   for (i=1;i<=n;i++) {   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     ip=indx[i];    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     sum=b[ip];      newm=savm;
     b[ip]=b[i];      /* Covariates have to be included here again */
     if (ii)       cov[2]=agefin;
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];    
     else if (sum) ii=i;        for (k=1; k<=cptcovn;k++) {
     b[i]=sum;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   }          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
   for (i=n;i>=1;i--) {        }
     sum=b[i];        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        for (k=1; k<=cptcovprod;k++)
     b[i]=sum/a[i][i];          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   }  
 }        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
 /************ Frequencies ********************/        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
 {  /* Some frequencies */  
        savm=oldm;
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;      oldm=newm;
   double ***freq; /* Frequencies */      maxmax=0.;
   double *pp;      for(j=1;j<=nlstate;j++){
   double pos, k2, dateintsum=0,k2cpt=0;        min=1.;
   FILE *ficresp;        max=0.;
   char fileresp[FILENAMELENGTH];        for(i=1; i<=nlstate; i++) {
            sumnew=0;
   pp=vector(1,nlstate);          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          prlim[i][j]= newm[i][j]/(1-sumnew);
   strcpy(fileresp,"p");          max=FMAX(max,prlim[i][j]);
   strcat(fileresp,fileres);          min=FMIN(min,prlim[i][j]);
   if((ficresp=fopen(fileresp,"w"))==NULL) {        }
     printf("Problem with prevalence resultfile: %s\n", fileresp);        maxmin=max-min;
     exit(0);        maxmax=FMAX(maxmax,maxmin);
   }      }
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      if(maxmax < ftolpl){
   j1=0;        return prlim;
       }
   j=cptcoveff;    }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  }
   
   for(k1=1; k1<=j;k1++){  /*************** transition probabilities ***************/ 
    for(i1=1; i1<=ncodemax[k1];i1++){  
        j1++;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);  {
          scanf("%d", i);*/    double s1, s2;
         for (i=-1; i<=nlstate+ndeath; i++)      /*double t34;*/
          for (jk=-1; jk<=nlstate+ndeath; jk++)      int i,j,j1, nc, ii, jj;
            for(m=agemin; m <= agemax+3; m++)  
              freq[i][jk][m]=0;      for(i=1; i<= nlstate; i++){
         for(j=1; j<i;j++){
         dateintsum=0;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
         k2cpt=0;            /*s2 += param[i][j][nc]*cov[nc];*/
        for (i=1; i<=imx; i++) {            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
          bool=1;  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
          if  (cptcovn>0) {          }
            for (z1=1; z1<=cptcoveff; z1++)          ps[i][j]=s2;
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
                bool=0;        }
          }        for(j=i+1; j<=nlstate+ndeath;j++){
          if (bool==1) {          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
            for(m=firstpass; m<=lastpass; m++){            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
              k2=anint[m][i]+(mint[m][i]/12.);  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
              if ((k2>=dateprev1) && (k2<=dateprev2)) {          }
                if(agev[m][i]==0) agev[m][i]=agemax+1;          ps[i][j]=s2;
                if(agev[m][i]==1) agev[m][i]=agemax+2;        }
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      }
                freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      /*ps[3][2]=1;*/
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {      
                  dateintsum=dateintsum+k2;      for(i=1; i<= nlstate; i++){
                  k2cpt++;        s1=0;
                }        for(j=1; j<i; j++)
           s1+=exp(ps[i][j]);
              }        for(j=i+1; j<=nlstate+ndeath; j++)
            }          s1+=exp(ps[i][j]);
          }        ps[i][i]=1./(s1+1.);
        }        for(j=1; j<i; j++)
                  ps[i][j]= exp(ps[i][j])*ps[i][i];
        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        for(j=i+1; j<=nlstate+ndeath; j++)
           ps[i][j]= exp(ps[i][j])*ps[i][i];
         if  (cptcovn>0) {        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
          fprintf(ficresp, "\n#********** Variable ");      } /* end i */
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      
        fprintf(ficresp, "**********\n#");      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         }        for(jj=1; jj<= nlstate+ndeath; jj++){
        for(i=1; i<=nlstate;i++)          ps[ii][jj]=0;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);          ps[ii][ii]=1;
        fprintf(ficresp, "\n");        }
              }
   for(i=(int)agemin; i <= (int)agemax+3; i++){      
     if(i==(int)agemax+3)  
       printf("Total");  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
     else  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       printf("Age %d", i);  /*         printf("ddd %lf ",ps[ii][jj]); */
     for(jk=1; jk <=nlstate ; jk++){  /*       } */
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  /*       printf("\n "); */
         pp[jk] += freq[jk][m][i];  /*        } */
     }  /*        printf("\n ");printf("%lf ",cov[2]); */
     for(jk=1; jk <=nlstate ; jk++){         /*
       for(m=-1, pos=0; m <=0 ; m++)        for(i=1; i<= npar; i++) printf("%f ",x[i]);
         pos += freq[jk][m][i];        goto end;*/
       if(pp[jk]>=1.e-10)      return ps;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  }
       else  
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  /**************** Product of 2 matrices ******************/
     }  
   double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
      for(jk=1; jk <=nlstate ; jk++){  {
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
         pp[jk] += freq[jk][m][i];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
      }    /* in, b, out are matrice of pointers which should have been initialized 
        before: only the contents of out is modified. The function returns
     for(jk=1,pos=0; jk <=nlstate ; jk++)       a pointer to pointers identical to out */
       pos += pp[jk];    long i, j, k;
     for(jk=1; jk <=nlstate ; jk++){    for(i=nrl; i<= nrh; i++)
       if(pos>=1.e-5)      for(k=ncolol; k<=ncoloh; k++)
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
       else          out[i][k] +=in[i][j]*b[j][k];
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  
       if( i <= (int) agemax){    return out;
         if(pos>=1.e-5){  }
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  
           probs[i][jk][j1]= pp[jk]/pos;  
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/  /************* Higher Matrix Product ***************/
         }  
       else  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  {
       }    /* Computes the transition matrix starting at age 'age' over 
     }       'nhstepm*hstepm*stepm' months (i.e. until
     for(jk=-1; jk <=nlstate+ndeath; jk++)       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
       for(m=-1; m <=nlstate+ndeath; m++)       nhstepm*hstepm matrices. 
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     if(i <= (int) agemax)       (typically every 2 years instead of every month which is too big 
       fprintf(ficresp,"\n");       for the memory).
     printf("\n");       Model is determined by parameters x and covariates have to be 
     }       included manually here. 
     }  
  }       */
   dateintmean=dateintsum/k2cpt;  
      int i, j, d, h, k;
   fclose(ficresp);    double **out, cov[NCOVMAX];
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    double **newm;
   free_vector(pp,1,nlstate);  
     /* Hstepm could be zero and should return the unit matrix */
   /* End of Freq */    for (i=1;i<=nlstate+ndeath;i++)
 }      for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
 /************ Prevalence ********************/        po[i][j][0]=(i==j ? 1.0 : 0.0);
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)      }
 {  /* Some frequencies */    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
      for(h=1; h <=nhstepm; h++){
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      for(d=1; d <=hstepm; d++){
   double ***freq; /* Frequencies */        newm=savm;
   double *pp;        /* Covariates have to be included here again */
   double pos, k2;        cov[1]=1.;
         cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   pp=vector(1,nlstate);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        for (k=1; k<=cptcovage;k++)
            cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        for (k=1; k<=cptcovprod;k++)
   j1=0;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
    
   j=cptcoveff;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
  for(k1=1; k1<=j;k1++){        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     for(i1=1; i1<=ncodemax[k1];i1++){                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       j1++;        savm=oldm;
          oldm=newm;
       for (i=-1; i<=nlstate+ndeath; i++)        }
         for (jk=-1; jk<=nlstate+ndeath; jk++)        for(i=1; i<=nlstate+ndeath; i++)
           for(m=agemin; m <= agemax+3; m++)        for(j=1;j<=nlstate+ndeath;j++) {
             freq[i][jk][m]=0;          po[i][j][h]=newm[i][j];
                /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       for (i=1; i<=imx; i++) {           */
         bool=1;        }
         if  (cptcovn>0) {    } /* end h */
           for (z1=1; z1<=cptcoveff; z1++)    return po;
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  }
               bool=0;  
         }  
         if (bool==1) {  /*************** log-likelihood *************/
           for(m=firstpass; m<=lastpass; m++){  double func( double *x)
             k2=anint[m][i]+(mint[m][i]/12.);  {
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    int i, ii, j, k, mi, d, kk;
               if(agev[m][i]==0) agev[m][i]=agemax+1;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
               if(agev[m][i]==1) agev[m][i]=agemax+2;    double **out;
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];    double sw; /* Sum of weights */
               /* freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];  */    double lli; /* Individual log likelihood */
             }    int s1, s2;
           }    double bbh, survp;
         }    long ipmx;
       }    /*extern weight */
         for(i=(int)agemin; i <= (int)agemax+3; i++){    /* We are differentiating ll according to initial status */
           for(jk=1; jk <=nlstate ; jk++){    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    /*for(i=1;i<imx;i++) 
               pp[jk] += freq[jk][m][i];      printf(" %d\n",s[4][i]);
           }    */
           for(jk=1; jk <=nlstate ; jk++){    cov[1]=1.;
             for(m=-1, pos=0; m <=0 ; m++)  
             pos += freq[jk][m][i];    for(k=1; k<=nlstate; k++) ll[k]=0.;
         }  
            if(mle==1){
          for(jk=1; jk <=nlstate ; jk++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
              pp[jk] += freq[jk][m][i];        for(mi=1; mi<= wav[i]-1; mi++){
          }          for (ii=1;ii<=nlstate+ndeath;ii++)
                      for (j=1;j<=nlstate+ndeath;j++){
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
          for(jk=1; jk <=nlstate ; jk++){                      }
            if( i <= (int) agemax){          for(d=0; d<dh[mi][i]; d++){
              if(pos>=1.e-5){            newm=savm;
                probs[i][jk][j1]= pp[jk]/pos;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              }            for (kk=1; kk<=cptcovage;kk++) {
            }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
          }            }
                      out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     }            savm=oldm;
   }            oldm=newm;
            } /* end mult */
          
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   free_vector(pp,1,nlstate);          /* But now since version 0.9 we anticipate for bias at large stepm.
             * If stepm is larger than one month (smallest stepm) and if the exact delay 
 }  /* End of Freq */           * (in months) between two waves is not a multiple of stepm, we rounded to 
            * the nearest (and in case of equal distance, to the lowest) interval but now
 /************* Waves Concatenation ***************/           * we keep into memory the bias bh[mi][i] and also the previous matrix product
            * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)           * probability in order to take into account the bias as a fraction of the way
 {           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.           * -stepm/2 to stepm/2 .
      Death is a valid wave (if date is known).           * For stepm=1 the results are the same as for previous versions of Imach.
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i           * For stepm > 1 the results are less biased than in previous versions. 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]           */
      and mw[mi+1][i]. dh depends on stepm.          s1=s[mw[mi][i]][i];
      */          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
   int i, mi, m;          /* bias bh is positive if real duration
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;           * is higher than the multiple of stepm and negative otherwise.
      double sum=0., jmean=0.;*/           */
           /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   int j, k=0,jk, ju, jl;          if( s2 > nlstate){ 
   double sum=0.;            /* i.e. if s2 is a death state and if the date of death is known 
   jmin=1e+5;               then the contribution to the likelihood is the probability to 
   jmax=-1;               die between last step unit time and current  step unit time, 
   jmean=0.;               which is also equal to probability to die before dh 
   for(i=1; i<=imx; i++){               minus probability to die before dh-stepm . 
     mi=0;               In version up to 0.92 likelihood was computed
     m=firstpass;          as if date of death was unknown. Death was treated as any other
     while(s[m][i] <= nlstate){          health state: the date of the interview describes the actual state
       if(s[m][i]>=1)          and not the date of a change in health state. The former idea was
         mw[++mi][i]=m;          to consider that at each interview the state was recorded
       if(m >=lastpass)          (healthy, disable or death) and IMaCh was corrected; but when we
         break;          introduced the exact date of death then we should have modified
       else          the contribution of an exact death to the likelihood. This new
         m++;          contribution is smaller and very dependent of the step unit
     }/* end while */          stepm. It is no more the probability to die between last interview
     if (s[m][i] > nlstate){          and month of death but the probability to survive from last
       mi++;     /* Death is another wave */          interview up to one month before death multiplied by the
       /* if(mi==0)  never been interviewed correctly before death */          probability to die within a month. Thanks to Chris
          /* Only death is a correct wave */          Jackson for correcting this bug.  Former versions increased
       mw[mi][i]=m;          mortality artificially. The bad side is that we add another loop
     }          which slows down the processing. The difference can be up to 10%
           lower mortality.
     wav[i]=mi;            */
     if(mi==0)            lli=log(out[s1][s2] - savm[s1][s2]);
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  
   }  
           } else if  (s2==-2) {
   for(i=1; i<=imx; i++){            for (j=1,survp=0. ; j<=nlstate; j++) 
     for(mi=1; mi<wav[i];mi++){              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       if (stepm <=0)            /*survp += out[s1][j]; */
         dh[mi][i]=1;            lli= log(survp);
       else{          }
         if (s[mw[mi+1][i]][i] > nlstate) {          
           if (agedc[i] < 2*AGESUP) {          else if  (s2==-4) { 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            for (j=3,survp=0. ; j<=nlstate; j++)  
           if(j==0) j=1;  /* Survives at least one month after exam */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           k=k+1;            lli= log(survp); 
           if (j >= jmax) jmax=j;          } 
           if (j <= jmin) jmin=j;  
           sum=sum+j;          else if  (s2==-5) { 
           /*if (j<0) printf("j=%d num=%d \n",j,i); */            for (j=1,survp=0. ; j<=2; j++)  
           }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
         }            lli= log(survp); 
         else{          } 
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          
           k=k+1;          else{
           if (j >= jmax) jmax=j;            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           else if (j <= jmin)jmin=j;            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */          } 
           sum=sum+j;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         }          /*if(lli ==000.0)*/
         jk= j/stepm;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
         jl= j -jk*stepm;          ipmx +=1;
         ju= j -(jk+1)*stepm;          sw += weight[i];
         if(jl <= -ju)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           dh[mi][i]=jk;        } /* end of wave */
         else      } /* end of individual */
           dh[mi][i]=jk+1;    }  else if(mle==2){
         if(dh[mi][i]==0)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           dh[mi][i]=1; /* At least one step */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
   }            for (j=1;j<=nlstate+ndeath;j++){
   jmean=sum/k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
  }            }
 /*********** Tricode ****************************/          for(d=0; d<=dh[mi][i]; d++){
 void tricode(int *Tvar, int **nbcode, int imx)            newm=savm;
 {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   int Ndum[20],ij=1, k, j, i;            for (kk=1; kk<=cptcovage;kk++) {
   int cptcode=0;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   cptcoveff=0;            }
              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for (k=0; k<19; k++) Ndum[k]=0;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   for (k=1; k<=7; k++) ncodemax[k]=0;            savm=oldm;
             oldm=newm;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          } /* end mult */
     for (i=1; i<=imx; i++) {        
       ij=(int)(covar[Tvar[j]][i]);          s1=s[mw[mi][i]][i];
       Ndum[ij]++;          s2=s[mw[mi+1][i]][i];
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          bbh=(double)bh[mi][i]/(double)stepm; 
       if (ij > cptcode) cptcode=ij;          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
     }          ipmx +=1;
           sw += weight[i];
     for (i=0; i<=cptcode; i++) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       if(Ndum[i]!=0) ncodemax[j]++;        } /* end of wave */
     }      } /* end of individual */
     ij=1;    }  else if(mle==3){  /* exponential inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     for (i=1; i<=ncodemax[j]; i++) {        for(mi=1; mi<= wav[i]-1; mi++){
       for (k=0; k<=19; k++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
         if (Ndum[k] != 0) {            for (j=1;j<=nlstate+ndeath;j++){
           nbcode[Tvar[j]][ij]=k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           ij++;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            }
         if (ij > ncodemax[j]) break;          for(d=0; d<dh[mi][i]; d++){
       }              newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   }              for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
  for (k=0; k<19; k++) Ndum[k]=0;            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  for (i=1; i<=ncovmodel-2; i++) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       ij=Tvar[i];            savm=oldm;
       Ndum[ij]++;            oldm=newm;
     }          } /* end mult */
         
  ij=1;          s1=s[mw[mi][i]][i];
  for (i=1; i<=10; i++) {          s2=s[mw[mi+1][i]][i];
    if((Ndum[i]!=0) && (i<=ncov)){          bbh=(double)bh[mi][i]/(double)stepm; 
      Tvaraff[ij]=i;          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
      ij++;          ipmx +=1;
    }          sw += weight[i];
  }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
          } /* end of wave */
     cptcoveff=ij-1;      } /* end of individual */
 }    }else if (mle==4){  /* ml=4 no inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 /*********** Health Expectancies ****************/        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          for (ii=1;ii<=nlstate+ndeath;ii++)
 {            for (j=1;j<=nlstate+ndeath;j++){
   /* Health expectancies */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j, nhstepm, hstepm, h, nstepm, k;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double age, agelim,hf;            }
   double ***p3mat;          for(d=0; d<dh[mi][i]; d++){
              newm=savm;
   fprintf(ficreseij,"# Health expectancies\n");            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficreseij,"# Age");            for (kk=1; kk<=cptcovage;kk++) {
   for(i=1; i<=nlstate;i++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(j=1; j<=nlstate;j++)            }
       fprintf(ficreseij," %1d-%1d",i,j);          
   fprintf(ficreseij,"\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   k=1;             /* For example stepm=6 months */            savm=oldm;
   hstepm=k*YEARM; /* (a) Every k years of age (in months), for example every k=2 years 24 m */            oldm=newm;
   hstepm=stepm;   /* or (b) We decided to compute the life expectancy with the smallest unit */          } /* end mult */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.        
      nhstepm is the number of hstepm from age to agelim          s1=s[mw[mi][i]][i];
      nstepm is the number of stepm from age to agelin.          s2=s[mw[mi+1][i]][i];
      Look at hpijx to understand the reason of that which relies in memory size          if( s2 > nlstate){ 
      and note for a fixed period like k years */            lli=log(out[s1][s2] - savm[s1][s2]);
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          }else{
      survival function given by stepm (the optimization length). Unfortunately it            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
      means that if the survival funtion is printed only each two years of age and if          }
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          ipmx +=1;
      results. So we changed our mind and took the option of the best precision.          sw += weight[i];
   */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   hstepm=hstepm/stepm; /* Typically in stepm units, if k= 2 years, = 2/6 months = 4 */  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         } /* end of wave */
   agelim=AGESUP;      } /* end of individual */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     /* nhstepm age range expressed in number of stepm */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     nstepm=(int) rint((agelim-age)*YEARM/stepm);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */        for(mi=1; mi<= wav[i]-1; mi++){
     if (stepm >= YEARM) hstepm=1;          for (ii=1;ii<=nlstate+ndeath;ii++)
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            for (j=1;j<=nlstate+ndeath;j++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* Computed by stepm unit matrices, product of hstepm matrices, stored              savm[ii][j]=(ii==j ? 1.0 : 0.0);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            }
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            for(d=0; d<dh[mi][i]; d++){
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */            newm=savm;
     for(i=1; i<=nlstate;i++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(j=1; j<=nlstate;j++)            for (kk=1; kk<=cptcovage;kk++) {
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;            }
           /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/          
         }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     fprintf(ficreseij,"%3.0f",age );                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(i=1; i<=nlstate;i++)            savm=oldm;
       for(j=1; j<=nlstate;j++){            oldm=newm;
         fprintf(ficreseij," %9.4f", eij[i][j][(int)age]);          } /* end mult */
       }        
     fprintf(ficreseij,"\n");          s1=s[mw[mi][i]][i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          s2=s[mw[mi+1][i]][i];
   }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 }          ipmx +=1;
           sw += weight[i];
 /************ Variance ******************/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
 {        } /* end of wave */
   /* Variance of health expectancies */      } /* end of individual */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    } /* End of if */
   double **newm;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   double **dnewm,**doldm;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   int i, j, nhstepm, hstepm, h;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   int k, cptcode;    return -l;
   double *xp;  }
   double **gp, **gm;  
   double ***gradg, ***trgradg;  /*************** log-likelihood *************/
   double ***p3mat;  double funcone( double *x)
   double age,agelim;  {
   int theta;    /* Same as likeli but slower because of a lot of printf and if */
     int i, ii, j, k, mi, d, kk;
    fprintf(ficresvij,"# Covariances of life expectancies\n");    double l, ll[NLSTATEMAX], cov[NCOVMAX];
   fprintf(ficresvij,"# Age");    double **out;
   for(i=1; i<=nlstate;i++)    double lli; /* Individual log likelihood */
     for(j=1; j<=nlstate;j++)    double llt;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    int s1, s2;
   fprintf(ficresvij,"\n");    double bbh, survp;
     /*extern weight */
   xp=vector(1,npar);    /* We are differentiating ll according to initial status */
   dnewm=matrix(1,nlstate,1,npar);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   doldm=matrix(1,nlstate,1,nlstate);    /*for(i=1;i<imx;i++) 
        printf(" %d\n",s[4][i]);
   hstepm=1*YEARM; /* Every year of age */    */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    cov[1]=1.;
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    for(k=1; k<=nlstate; k++) ll[k]=0.;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     if (stepm >= YEARM) hstepm=1;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(mi=1; mi<= wav[i]-1; mi++){
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        for (ii=1;ii<=nlstate+ndeath;ii++)
     gp=matrix(0,nhstepm,1,nlstate);          for (j=1;j<=nlstate+ndeath;j++){
     gm=matrix(0,nhstepm,1,nlstate);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(theta=1; theta <=npar; theta++){          }
       for(i=1; i<=npar; i++){ /* Computes gradient */        for(d=0; d<dh[mi][i]; d++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          newm=savm;
       }          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for (kk=1; kk<=cptcovage;kk++) {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }
       if (popbased==1) {          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(i=1; i<=nlstate;i++)                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           prlim[i][i]=probs[(int)age][i][ij];          savm=oldm;
       }          oldm=newm;
          } /* end mult */
       for(j=1; j<= nlstate; j++){        
         for(h=0; h<=nhstepm; h++){        s1=s[mw[mi][i]][i];
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        s2=s[mw[mi+1][i]][i];
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        bbh=(double)bh[mi][i]/(double)stepm; 
         }        /* bias is positive if real duration
       }         * is higher than the multiple of stepm and negative otherwise.
             */
       for(i=1; i<=npar; i++) /* Computes gradient */        if( s2 > nlstate && (mle <5) ){  /* Jackson */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          lli=log(out[s1][s2] - savm[s1][s2]);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          } else if  (s2==-2) {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          for (j=1,survp=0. ; j<=nlstate; j++) 
              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       if (popbased==1) {          lli= log(survp);
         for(i=1; i<=nlstate;i++)        }else if (mle==1){
           prlim[i][i]=probs[(int)age][i][ij];          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       }        } else if(mle==2){
           lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       for(j=1; j<= nlstate; j++){        } else if(mle==3){  /* exponential inter-extrapolation */
         for(h=0; h<=nhstepm; h++){          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        } else if (mle==4){  /* mle=4 no inter-extrapolation */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          lli=log(out[s1][s2]); /* Original formula */
         }        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       }          lli=log(out[s1][s2]); /* Original formula */
         } /* End of if */
       for(j=1; j<= nlstate; j++)        ipmx +=1;
         for(h=0; h<=nhstepm; h++){        sw += weight[i];
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
     } /* End theta */        if(globpr){
           fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     for(h=0; h<=nhstepm; h++)                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       for(j=1; j<=nlstate;j++)          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
         for(theta=1; theta <=npar; theta++)            llt +=ll[k]*gipmx/gsw;
           trgradg[h][j][theta]=gradg[h][theta][j];            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           }
     for(i=1;i<=nlstate;i++)          fprintf(ficresilk," %10.6f\n", -llt);
       for(j=1;j<=nlstate;j++)        }
         vareij[i][j][(int)age] =0.;      } /* end of wave */
     for(h=0;h<=nhstepm;h++){    } /* end of individual */
       for(k=0;k<=nhstepm;k++){    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
         for(i=1;i<=nlstate;i++)    if(globpr==0){ /* First time we count the contributions and weights */
           for(j=1;j<=nlstate;j++)      gipmx=ipmx;
             vareij[i][j][(int)age] += doldm[i][j];      gsw=sw;
       }    }
     }    return -l;
     h=1;  }
     if (stepm >= YEARM) h=stepm/YEARM;  
     fprintf(ficresvij,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)  /*************** function likelione ***********/
       for(j=1; j<=nlstate;j++){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);  {
       }    /* This routine should help understanding what is done with 
     fprintf(ficresvij,"\n");       the selection of individuals/waves and
     free_matrix(gp,0,nhstepm,1,nlstate);       to check the exact contribution to the likelihood.
     free_matrix(gm,0,nhstepm,1,nlstate);       Plotting could be done.
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);     */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    int k;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   } /* End age */    if(*globpri !=0){ /* Just counts and sums, no printings */
        strcpy(fileresilk,"ilk"); 
   free_vector(xp,1,npar);      strcat(fileresilk,fileres);
   free_matrix(doldm,1,nlstate,1,npar);      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   free_matrix(dnewm,1,nlstate,1,nlstate);        printf("Problem with resultfile: %s\n", fileresilk);
         fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
 }      }
       fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
 /************ Variance of prevlim ******************/      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
 {      for(k=1; k<=nlstate; k++) 
   /* Variance of prevalence limit */        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   double **newm;    }
   double **dnewm,**doldm;  
   int i, j, nhstepm, hstepm;    *fretone=(*funcone)(p);
   int k, cptcode;    if(*globpri !=0){
   double *xp;      fclose(ficresilk);
   double *gp, *gm;      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   double **gradg, **trgradg;      fflush(fichtm); 
   double age,agelim;    } 
   int theta;    return;
      }
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)  /*********** Maximum Likelihood Estimation ***************/
       fprintf(ficresvpl," %1d-%1d",i,i);  
   fprintf(ficresvpl,"\n");  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   {
   xp=vector(1,npar);    int i,j, iter;
   dnewm=matrix(1,nlstate,1,npar);    double **xi;
   doldm=matrix(1,nlstate,1,nlstate);    double fret;
      double fretone; /* Only one call to likelihood */
   hstepm=1*YEARM; /* Every year of age */    /*  char filerespow[FILENAMELENGTH];*/
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    xi=matrix(1,npar,1,npar);
   agelim = AGESUP;    for (i=1;i<=npar;i++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (j=1;j<=npar;j++)
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        xi[i][j]=(i==j ? 1.0 : 0.0);
     if (stepm >= YEARM) hstepm=1;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    strcpy(filerespow,"pow"); 
     gradg=matrix(1,npar,1,nlstate);    strcat(filerespow,fileres);
     gp=vector(1,nlstate);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     gm=vector(1,nlstate);      printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     for(theta=1; theta <=npar; theta++){    }
       for(i=1; i<=npar; i++){ /* Computes gradient */    fprintf(ficrespow,"# Powell\n# iter -2*LL");
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    for (i=1;i<=nlstate;i++)
       }      for(j=1;j<=nlstate+ndeath;j++)
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       for(i=1;i<=nlstate;i++)    fprintf(ficrespow,"\n");
         gp[i] = prlim[i][i];  
        powell(p,xi,npar,ftol,&iter,&fret,func);
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    free_matrix(xi,1,npar,1,npar);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fclose(ficrespow);
       for(i=1;i<=nlstate;i++)    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         gm[i] = prlim[i][i];    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       for(i=1;i<=nlstate;i++)  
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  }
     } /* End theta */  
   /**** Computes Hessian and covariance matrix ***/
     trgradg =matrix(1,nlstate,1,npar);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   {
     for(j=1; j<=nlstate;j++)    double  **a,**y,*x,pd;
       for(theta=1; theta <=npar; theta++)    double **hess;
         trgradg[j][theta]=gradg[theta][j];    int i, j,jk;
     int *indx;
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] =0.;    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    void lubksb(double **a, int npar, int *indx, double b[]) ;
     for(i=1;i<=nlstate;i++)    void ludcmp(double **a, int npar, int *indx, double *d) ;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    double gompertz(double p[]);
     hess=matrix(1,npar,1,npar);
     fprintf(ficresvpl,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)    printf("\nCalculation of the hessian matrix. Wait...\n");
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     fprintf(ficresvpl,"\n");    for (i=1;i<=npar;i++){
     free_vector(gp,1,nlstate);      printf("%d",i);fflush(stdout);
     free_vector(gm,1,nlstate);      fprintf(ficlog,"%d",i);fflush(ficlog);
     free_matrix(gradg,1,npar,1,nlstate);     
     free_matrix(trgradg,1,nlstate,1,npar);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   } /* End age */      
       /*  printf(" %f ",p[i]);
   free_vector(xp,1,npar);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   free_matrix(doldm,1,nlstate,1,npar);    }
   free_matrix(dnewm,1,nlstate,1,nlstate);    
     for (i=1;i<=npar;i++) {
 }      for (j=1;j<=npar;j++)  {
         if (j>i) { 
 /************ Variance of one-step probabilities  ******************/          printf(".%d%d",i,j);fflush(stdout);
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
 {          hess[i][j]=hessij(p,delti,i,j,func,npar);
   int i, j;          
   int k=0, cptcode;          hess[j][i]=hess[i][j];    
   double **dnewm,**doldm;          /*printf(" %lf ",hess[i][j]);*/
   double *xp;        }
   double *gp, *gm;      }
   double **gradg, **trgradg;    }
   double age,agelim, cov[NCOVMAX];    printf("\n");
   int theta;    fprintf(ficlog,"\n");
   char fileresprob[FILENAMELENGTH];  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   strcpy(fileresprob,"prob");    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   strcat(fileresprob,fileres);    
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    a=matrix(1,npar,1,npar);
     printf("Problem with resultfile: %s\n", fileresprob);    y=matrix(1,npar,1,npar);
   }    x=vector(1,npar);
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);    indx=ivector(1,npar);
      for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   xp=vector(1,npar);    ludcmp(a,npar,indx,&pd);
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    for (j=1;j<=npar;j++) {
        for (i=1;i<=npar;i++) x[i]=0;
   cov[1]=1;      x[j]=1;
   for (age=bage; age<=fage; age ++){      lubksb(a,npar,indx,x);
     cov[2]=age;      for (i=1;i<=npar;i++){ 
     gradg=matrix(1,npar,1,9);        matcov[i][j]=x[i];
     trgradg=matrix(1,9,1,npar);      }
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    }
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));  
        printf("\n#Hessian matrix#\n");
     for(theta=1; theta <=npar; theta++){    fprintf(ficlog,"\n#Hessian matrix#\n");
       for(i=1; i<=npar; i++)    for (i=1;i<=npar;i++) { 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for (j=1;j<=npar;j++) { 
              printf("%.3e ",hess[i][j]);
       pmij(pmmij,cov,ncovmodel,xp,nlstate);        fprintf(ficlog,"%.3e ",hess[i][j]);
          }
       k=0;      printf("\n");
       for(i=1; i<= (nlstate+ndeath); i++){      fprintf(ficlog,"\n");
         for(j=1; j<=(nlstate+ndeath);j++){    }
            k=k+1;  
           gp[k]=pmmij[i][j];    /* Recompute Inverse */
         }    for (i=1;i<=npar;i++)
       }      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     ludcmp(a,npar,indx,&pd);
       for(i=1; i<=npar; i++)  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    /*  printf("\n#Hessian matrix recomputed#\n");
      
     for (j=1;j<=npar;j++) {
       pmij(pmmij,cov,ncovmodel,xp,nlstate);      for (i=1;i<=npar;i++) x[i]=0;
       k=0;      x[j]=1;
       for(i=1; i<=(nlstate+ndeath); i++){      lubksb(a,npar,indx,x);
         for(j=1; j<=(nlstate+ndeath);j++){      for (i=1;i<=npar;i++){ 
           k=k+1;        y[i][j]=x[i];
           gm[k]=pmmij[i][j];        printf("%.3e ",y[i][j]);
         }        fprintf(ficlog,"%.3e ",y[i][j]);
       }      }
            printf("\n");
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)      fprintf(ficlog,"\n");
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      }
     }    */
   
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    free_matrix(a,1,npar,1,npar);
       for(theta=1; theta <=npar; theta++)    free_matrix(y,1,npar,1,npar);
       trgradg[j][theta]=gradg[theta][j];    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    free_matrix(hess,1,npar,1,npar);
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);  
   
      pmij(pmmij,cov,ncovmodel,x,nlstate);  }
   
      k=0;  /*************** hessian matrix ****************/
      for(i=1; i<=(nlstate+ndeath); i++){  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
        for(j=1; j<=(nlstate+ndeath);j++){  {
          k=k+1;    int i;
          gm[k]=pmmij[i][j];    int l=1, lmax=20;
         }    double k1,k2;
      }    double p2[NPARMAX+1];
          double res;
      /*printf("\n%d ",(int)age);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    double fx;
            int k=0,kmax=10;
     double l1;
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));  
      }*/    fx=func(x);
     for (i=1;i<=npar;i++) p2[i]=x[i];
   fprintf(ficresprob,"\n%d ",(int)age);    for(l=0 ; l <=lmax; l++){
       l1=pow(10,l);
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      delts=delt;
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      for(k=1 ; k <kmax; k=k+1){
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        delt = delta*(l1*k);
   }        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));        p2[theta]=x[theta]-delt;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));        k2=func(p2)-fx;
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        /*res= (k1-2.0*fx+k2)/delt/delt; */
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
 }        
  free_vector(xp,1,npar);  #ifdef DEBUG
 fclose(ficresprob);        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
 }  #endif
         /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
 /******************* Printing html file ***********/        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, int lastpass, int stepm, int weightopt, char model[],int imx,int jmin, int jmax, double jmeanint,char optionfile[],char optionfilehtm[],char rfileres[] ){          k=kmax;
   int jj1, k1, i1, cpt;        }
   FILE *fichtm;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   /*char optionfilehtm[FILENAMELENGTH];*/          k=kmax; l=lmax*10.;
         }
   strcpy(optionfilehtm,optionfile);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   strcat(optionfilehtm,".htm");          delts=delt;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        }
     printf("Problem with %s \n",optionfilehtm), exit(0);      }
   }    }
     delti[theta]=delts;
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.71c </font> <hr size=\"2\" color=\"#EC5E5E\">    return res; 
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    
   }
 Total number of observations=%d <br>  
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
 <hr  size=\"2\" color=\"#EC5E5E\">  {
 <li>Outputs files<br><br>\n    int i;
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    int l=1, l1, lmax=20;
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>    double k1,k2,k3,k4,res,fx;
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>    double p2[NPARMAX+1];
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    int k;
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    fx=func(x);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    for (k=1; k<=2; k++) {
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>      for (i=1;i<=npar;i++) p2[i]=x[i];
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>      p2[thetai]=x[thetai]+delti[thetai]/k;
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
         - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>      k1=func(p2)-fx;
         <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);    
        p2[thetai]=x[thetai]+delti[thetai]/k;
 fprintf(fichtm," <li>Graphs</li><p>");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k2=func(p2)-fx;
  m=cptcoveff;    
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
  jj1=0;      k3=func(p2)-fx;
  for(k1=1; k1<=m;k1++){    
    for(i1=1; i1<=ncodemax[k1];i1++){      p2[thetai]=x[thetai]-delti[thetai]/k;
        jj1++;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
        if (cptcovn > 0) {      k4=func(p2)-fx;
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
          for (cpt=1; cpt<=cptcoveff;cpt++)  #ifdef DEBUG
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
        }  #endif
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>    }
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        return res;
        for(cpt=1; cpt<nlstate;cpt++){  }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>  
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  /************** Inverse of matrix **************/
        }  void ludcmp(double **a, int n, int *indx, double *d) 
     for(cpt=1; cpt<=nlstate;cpt++) {  { 
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    int i,imax,j,k; 
 interval) in state (%d): v%s%d%d.gif <br>    double big,dum,sum,temp; 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      double *vv; 
      }   
      for(cpt=1; cpt<=nlstate;cpt++) {    vv=vector(1,n); 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    *d=1.0; 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    for (i=1;i<=n;i++) { 
      }      big=0.0; 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      for (j=1;j<=n;j++) 
 health expectancies in states (1) and (2): e%s%d.gif<br>        if ((temp=fabs(a[i][j])) > big) big=temp; 
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
 fprintf(fichtm,"\n</body>");      vv[i]=1.0/big; 
    }    } 
    }    for (j=1;j<=n;j++) { 
 fclose(fichtm);      for (i=1;i<j;i++) { 
 }        sum=a[i][j]; 
         for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
 /******************* Gnuplot file **************/        a[i][j]=sum; 
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double agemin, double agemaxpar, double fage , char pathc[], double p[]){      } 
       big=0.0; 
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;      for (i=j;i<=n;i++) { 
         sum=a[i][j]; 
   strcpy(optionfilegnuplot,optionfilefiname);        for (k=1;k<j;k++) 
   strcat(optionfilegnuplot,".plt");          sum -= a[i][k]*a[k][j]; 
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {        a[i][j]=sum; 
     printf("Problem with file %s",optionfilegnuplot);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   }          big=dum; 
           imax=i; 
 #ifdef windows        } 
     fprintf(ficgp,"cd \"%s\" \n",pathc);      } 
 #endif      if (j != imax) { 
 m=pow(2,cptcoveff);        for (k=1;k<=n;k++) { 
            dum=a[imax][k]; 
  /* 1eme*/          a[imax][k]=a[j][k]; 
   for (cpt=1; cpt<= nlstate ; cpt ++) {          a[j][k]=dum; 
    for (k1=1; k1<= m ; k1 ++) {        } 
         *d = -(*d); 
 #ifdef windows        vv[imax]=vv[j]; 
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);      } 
 #endif      indx[j]=imax; 
 #ifdef unix      if (a[j][j] == 0.0) a[j][j]=TINY; 
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);      if (j != n) { 
 #endif        dum=1.0/(a[j][j]); 
         for (i=j+1;i<=n;i++) a[i][j] *= dum; 
 for (i=1; i<= nlstate ; i ++) {      } 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");    free_vector(vv,1,n);  /* Doesn't work */
 }  ;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);  } 
     for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  void lubksb(double **a, int n, int *indx, double b[]) 
   else fprintf(ficgp," \%%*lf (\%%*lf)");  { 
 }    int i,ii=0,ip,j; 
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    double sum; 
      for (i=1; i<= nlstate ; i ++) {   
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    for (i=1;i<=n;i++) { 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      ip=indx[i]; 
 }        sum=b[ip]; 
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));      b[ip]=b[i]; 
 #ifdef unix      if (ii) 
 fprintf(ficgp,"\nset ter gif small size 400,300");        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
 #endif      else if (sum) ii=i; 
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      b[i]=sum; 
    }    } 
   }    for (i=n;i>=1;i--) { 
   /*2 eme*/      sum=b[i]; 
       for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   for (k1=1; k1<= m ; k1 ++) {      b[i]=sum/a[i][i]; 
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    } 
      } 
     for (i=1; i<= nlstate+1 ; i ++) {  
       k=2*i;  void pstamp(FILE *fichier)
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);  {
       for (j=1; j<= nlstate+1 ; j ++) {    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }    /************ Frequencies ********************/
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);  {  /* Some frequencies */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    
       for (j=1; j<= nlstate+1 ; j ++) {    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    int first;
         else fprintf(ficgp," \%%*lf (\%%*lf)");    double ***freq; /* Frequencies */
 }      double *pp, **prop;
       fprintf(ficgp,"\" t\"\" w l 0,");    double pos,posprop, k2, dateintsum=0,k2cpt=0;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    char fileresp[FILENAMELENGTH];
       for (j=1; j<= nlstate+1 ; j ++) {    
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    pp=vector(1,nlstate);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    prop=matrix(1,nlstate,iagemin,iagemax+3);
 }      strcpy(fileresp,"p");
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    strcat(fileresp,fileres);
       else fprintf(ficgp,"\" t\"\" w l 0,");    if((ficresp=fopen(fileresp,"w"))==NULL) {
     }      printf("Problem with prevalence resultfile: %s\n", fileresp);
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   }      exit(0);
      }
   /*3eme*/    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
     j1=0;
   for (k1=1; k1<= m ; k1 ++) {    
     for (cpt=1; cpt<= nlstate ; cpt ++) {    j=cptcoveff;
       k=2+nlstate*(cpt-1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);  
       for (i=1; i< nlstate ; i ++) {    first=1;
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);  
       }    for(k1=1; k1<=j;k1++){
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      for(i1=1; i1<=ncodemax[k1];i1++){
     }        j1++;
     }        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
            scanf("%d", i);*/
   /* CV preval stat */        for (i=-5; i<=nlstate+ndeath; i++)  
     for (k1=1; k1<= m ; k1 ++) {          for (jk=-5; jk<=nlstate+ndeath; jk++)  
     for (cpt=1; cpt<nlstate ; cpt ++) {            for(m=iagemin; m <= iagemax+3; m++)
       k=3;              freq[i][jk][m]=0;
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemaxpar,fileres,k1,k+cpt+1,k+1);  
       for (i=1; i<=nlstate; i++)  
       for (i=1; i< nlstate ; i ++)        for(m=iagemin; m <= iagemax+3; m++)
         fprintf(ficgp,"+$%d",k+i+1);          prop[i][m]=0;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);        
              dateintsum=0;
       l=3+(nlstate+ndeath)*cpt;        k2cpt=0;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);        for (i=1; i<=imx; i++) {
       for (i=1; i< nlstate ; i ++) {          bool=1;
         l=3+(nlstate+ndeath)*cpt;          if  (cptcovn>0) {
         fprintf(ficgp,"+$%d",l+i+1);            for (z1=1; z1<=cptcoveff; z1++) 
       }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                  bool=0;
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          }
     }          if (bool==1){
   }              for(m=firstpass; m<=lastpass; m++){
                k2=anint[m][i]+(mint[m][i]/12.);
   /* proba elementaires */              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
    for(i=1,jk=1; i <=nlstate; i++){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     for(k=1; k <=(nlstate+ndeath); k++){                if(agev[m][i]==1) agev[m][i]=iagemax+2;
       if (k != i) {                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
         for(j=1; j <=ncovmodel; j++){                if (m<lastpass) {
                          freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
           jk++;                }
           fprintf(ficgp,"\n");                
         }                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
       }                  dateintsum=dateintsum+k2;
     }                  k2cpt++;
     }                }
                 /*}*/
     for(jk=1; jk <=m; jk++) {            }
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemaxpar);          }
    i=1;        }
    for(k2=1; k2<=nlstate; k2++) {         
      k3=i;        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
      for(k=1; k<=(nlstate+ndeath); k++) {        pstamp(ficresp);
        if (k != k2){        if  (cptcovn>0) {
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          fprintf(ficresp, "\n#********** Variable "); 
 ij=1;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         for(j=3; j <=ncovmodel; j++) {          fprintf(ficresp, "**********\n#");
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        }
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        for(i=1; i<=nlstate;i++) 
             ij++;          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
           }        fprintf(ficresp, "\n");
           else        
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        for(i=iagemin; i <= iagemax+3; i++){
         }          if(i==iagemax+3){
           fprintf(ficgp,")/(1");            fprintf(ficlog,"Total");
                  }else{
         for(k1=1; k1 <=nlstate; k1++){              if(first==1){
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);              first=0;
 ij=1;              printf("See log file for details...\n");
           for(j=3; j <=ncovmodel; j++){            }
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {            fprintf(ficlog,"Age %d", i);
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          }
             ij++;          for(jk=1; jk <=nlstate ; jk++){
           }            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
           else              pp[jk] += freq[jk][m][i]; 
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          }
           }          for(jk=1; jk <=nlstate ; jk++){
           fprintf(ficgp,")");            for(m=-1, pos=0; m <=0 ; m++)
         }              pos += freq[jk][m][i];
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);            if(pp[jk]>=1.e-10){
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");              if(first==1){
         i=i+ncovmodel;              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
        }              }
      }              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
    }            }else{
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);              if(first==1)
    }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                  fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   fclose(ficgp);            }
 }  /* end gnuplot */          }
   
           for(jk=1; jk <=nlstate ; jk++){
 /*************** Moving average **************/            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
 void movingaverage(double agedeb, double fage,double agemin, double ***mobaverage){              pp[jk] += freq[jk][m][i];
           }       
   int i, cpt, cptcod;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     for (agedeb=agemin; agedeb<=fage; agedeb++)            pos += pp[jk];
       for (i=1; i<=nlstate;i++)            posprop += prop[jk][i];
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)          }
           mobaverage[(int)agedeb][i][cptcod]=0.;          for(jk=1; jk <=nlstate ; jk++){
                if(pos>=1.e-5){
     for (agedeb=agemin+4; agedeb<=fage; agedeb++){              if(first==1)
       for (i=1; i<=nlstate;i++){                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           for (cpt=0;cpt<=4;cpt++){            }else{
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];              if(first==1)
           }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
         }            }
       }            if( i <= iagemax){
     }              if(pos>=1.e-5){
                    fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
 }                /*probs[i][jk][j1]= pp[jk]/pos;*/
                 /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
               }
 /************** Forecasting ******************/              else
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double agemin, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
              }
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;          }
   int *popage;          
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;          for(jk=-1; jk <=nlstate+ndeath; jk++)
   double *popeffectif,*popcount;            for(m=-1; m <=nlstate+ndeath; m++)
   double ***p3mat;              if(freq[jk][m][i] !=0 ) {
   char fileresf[FILENAMELENGTH];              if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
  agelim=AGESUP;                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;              }
           if(i <= iagemax)
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);            fprintf(ficresp,"\n");
            if(first==1)
              printf("Others in log...\n");
   strcpy(fileresf,"f");          fprintf(ficlog,"\n");
   strcat(fileresf,fileres);        }
   if((ficresf=fopen(fileresf,"w"))==NULL) {      }
     printf("Problem with forecast resultfile: %s\n", fileresf);    }
   }    dateintmean=dateintsum/k2cpt; 
   printf("Computing forecasting: result on file '%s' \n", fileresf);   
     fclose(ficresp);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     free_vector(pp,1,nlstate);
   if (mobilav==1) {    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /* End of Freq */
     movingaverage(agedeb, fage, agemin, mobaverage);  }
   }  
   /************ Prevalence ********************/
   stepsize=(int) (stepm+YEARM-1)/YEARM;  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   if (stepm<=12) stepsize=1;  {  
      /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   agelim=AGESUP;       in each health status at the date of interview (if between dateprev1 and dateprev2).
         We still use firstpass and lastpass as another selection.
   hstepm=1;    */
   hstepm=hstepm/stepm;   
   yp1=modf(dateintmean,&yp);    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
   anprojmean=yp;    double ***freq; /* Frequencies */
   yp2=modf((yp1*12),&yp);    double *pp, **prop;
   mprojmean=yp;    double pos,posprop; 
   yp1=modf((yp2*30.5),&yp);    double  y2; /* in fractional years */
   jprojmean=yp;    int iagemin, iagemax;
   if(jprojmean==0) jprojmean=1;  
   if(mprojmean==0) jprojmean=1;    iagemin= (int) agemin;
      iagemax= (int) agemax;
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);    /*pp=vector(1,nlstate);*/
      prop=matrix(1,nlstate,iagemin,iagemax+3); 
   for(cptcov=1;cptcov<=i2;cptcov++){    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    j1=0;
       k=k+1;    
       fprintf(ficresf,"\n#******");    j=cptcoveff;
       for(j=1;j<=cptcoveff;j++) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    
       }    for(k1=1; k1<=j;k1++){
       fprintf(ficresf,"******\n");      for(i1=1; i1<=ncodemax[k1];i1++){
       fprintf(ficresf,"# StartingAge FinalAge");        j1++;
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);        
              for (i=1; i<=nlstate; i++)  
                for(m=iagemin; m <= iagemax+3; m++)
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {            prop[i][m]=0.0;
         fprintf(ficresf,"\n");       
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);          for (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){          if  (cptcovn>0) {
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            for (z1=1; z1<=cptcoveff; z1++) 
           nhstepm = nhstepm/hstepm;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                          bool=0;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          } 
           oldm=oldms;savm=savms;          if (bool==1) { 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
                      y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
           for (h=0; h<=nhstepm; h++){              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
             if (h==(int) (calagedate+YEARM*cpt)) {                if(agev[m][i]==0) agev[m][i]=iagemax+1;
               fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
             }                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
             for(j=1; j<=nlstate+ndeath;j++) {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
               kk1=0.;kk2=0;                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
               for(i=1; i<=nlstate;i++) {                                prop[s[m][i]][(int)agev[m][i]] += weight[i];
                 if (mobilav==1)                  prop[s[m][i]][iagemax+3] += weight[i]; 
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];                } 
                 else {              }
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];            } /* end selection of waves */
                 }          }
                        }
               }        for(i=iagemin; i <= iagemax+3; i++){  
               if (h==(int)(calagedate+12*cpt)){          
                 fprintf(ficresf," %.3f", kk1);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
                                    posprop += prop[jk][i]; 
               }          } 
             }  
           }          for(jk=1; jk <=nlstate ; jk++){     
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            if( i <=  iagemax){ 
         }              if(posprop>=1.e-5){ 
       }                probs[i][jk][j1]= prop[jk][i]/posprop;
     }              } 
   }            } 
                  }/* end jk */ 
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        }/* end i */ 
       } /* end i1 */
   fclose(ficresf);    } /* end k1 */
 }    
 /************** Forecasting ******************/    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double agemin, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){    /*free_vector(pp,1,nlstate);*/
      free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;  }  /* End of prevalence */
   int *popage;  
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  /************* Waves Concatenation ***************/
   double *popeffectif,*popcount;  
   double ***p3mat,***tabpop,***tabpopprev;  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
   char filerespop[FILENAMELENGTH];  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);       Death is a valid wave (if date is known).
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   agelim=AGESUP;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;       and mw[mi+1][i]. dh depends on stepm.
         */
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  
      int i, mi, m;
      /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
   strcpy(filerespop,"pop");       double sum=0., jmean=0.;*/
   strcat(filerespop,fileres);    int first;
   if((ficrespop=fopen(filerespop,"w"))==NULL) {    int j, k=0,jk, ju, jl;
     printf("Problem with forecast resultfile: %s\n", filerespop);    double sum=0.;
   }    first=0;
   printf("Computing forecasting: result on file '%s' \n", filerespop);    jmin=1e+5;
     jmax=-1;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    jmean=0.;
     for(i=1; i<=imx; i++){
   if (mobilav==1) {      mi=0;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      m=firstpass;
     movingaverage(agedeb, fage, agemin, mobaverage);      while(s[m][i] <= nlstate){
   }        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
           mw[++mi][i]=m;
   stepsize=(int) (stepm+YEARM-1)/YEARM;        if(m >=lastpass)
   if (stepm<=12) stepsize=1;          break;
          else
   agelim=AGESUP;          m++;
        }/* end while */
   hstepm=1;      if (s[m][i] > nlstate){
   hstepm=hstepm/stepm;        mi++;     /* Death is another wave */
          /* if(mi==0)  never been interviewed correctly before death */
   if (popforecast==1) {           /* Only death is a correct wave */
     if((ficpop=fopen(popfile,"r"))==NULL) {        mw[mi][i]=m;
       printf("Problem with population file : %s\n",popfile);exit(0);      }
     }  
     popage=ivector(0,AGESUP);      wav[i]=mi;
     popeffectif=vector(0,AGESUP);      if(mi==0){
     popcount=vector(0,AGESUP);        nbwarn++;
            if(first==0){
     i=1;            printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;          first=1;
            }
     imx=i;        if(first==1){
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
   }        }
       } /* end mi==0 */
   for(cptcov=1;cptcov<=i2;cptcov++){    } /* End individuals */
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
       k=k+1;    for(i=1; i<=imx; i++){
       fprintf(ficrespop,"\n#******");      for(mi=1; mi<wav[i];mi++){
       for(j=1;j<=cptcoveff;j++) {        if (stepm <=0)
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          dh[mi][i]=1;
       }        else{
       fprintf(ficrespop,"******\n");          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       fprintf(ficrespop,"# Age");            if (agedc[i] < 2*AGESUP) {
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       if (popforecast==1)  fprintf(ficrespop," [Population]");              if(j==0) j=1;  /* Survives at least one month after exam */
                    else if(j<0){
       for (cpt=0; cpt<=0;cpt++) {                nberr++;
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);                  printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                        j=1; /* Temporary Dangerous patch */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
           nhstepm = nhstepm/hstepm;                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
                        }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              k=k+1;
           oldm=oldms;savm=savms;              if (j >= jmax){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                  jmax=j;
                        ijmax=i;
           for (h=0; h<=nhstepm; h++){              }
             if (h==(int) (calagedate+YEARM*cpt)) {              if (j <= jmin){
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);                jmin=j;
             }                ijmin=i;
             for(j=1; j<=nlstate+ndeath;j++) {              }
               kk1=0.;kk2=0;              sum=sum+j;
               for(i=1; i<=nlstate;i++) {                            /*if (j<0) printf("j=%d num=%d \n",j,i);*/
                 if (mobilav==1)              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];            }
                 else {          }
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];          else{
                 }            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
               }  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
               if (h==(int)(calagedate+12*cpt)){  
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;            k=k+1;
                   /*fprintf(ficrespop," %.3f", kk1);            if (j >= jmax) {
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/              jmax=j;
               }              ijmax=i;
             }            }
             for(i=1; i<=nlstate;i++){            else if (j <= jmin){
               kk1=0.;              jmin=j;
                 for(j=1; j<=nlstate;j++){              ijmin=i;
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];            }
                 }            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
             }            if(j<0){
               nberr++;
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
           }            }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            sum=sum+j;
         }          }
       }          jk= j/stepm;
            jl= j -jk*stepm;
   /******/          ju= j -(jk+1)*stepm;
           if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {            if(jl==0){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);                dh[mi][i]=jk;
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){              bh[mi][i]=0;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            }else{ /* We want a negative bias in order to only have interpolation ie
           nhstepm = nhstepm/hstepm;                    * at the price of an extra matrix product in likelihood */
                        dh[mi][i]=jk+1;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              bh[mi][i]=ju;
           oldm=oldms;savm=savms;            }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            }else{
           for (h=0; h<=nhstepm; h++){            if(jl <= -ju){
             if (h==(int) (calagedate+YEARM*cpt)) {              dh[mi][i]=jk;
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);              bh[mi][i]=jl;       /* bias is positive if real duration
             }                                   * is higher than the multiple of stepm and negative otherwise.
             for(j=1; j<=nlstate+ndeath;j++) {                                   */
               kk1=0.;kk2=0;            }
               for(i=1; i<=nlstate;i++) {                          else{
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];                  dh[mi][i]=jk+1;
               }              bh[mi][i]=ju;
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);            }
             }            if(dh[mi][i]==0){
           }              dh[mi][i]=1; /* At least one step */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              bh[mi][i]=ju; /* At least one step */
         }              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
       }            }
    }          } /* end if mle */
   }        }
        } /* end wave */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    }
     jmean=sum/k;
   if (popforecast==1) {    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
     free_ivector(popage,0,AGESUP);    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
     free_vector(popeffectif,0,AGESUP);   }
     free_vector(popcount,0,AGESUP);  
   }  /*********** Tricode ****************************/
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  void tricode(int *Tvar, int **nbcode, int imx)
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  {
   fclose(ficrespop);    
 }    int Ndum[20],ij=1, k, j, i, maxncov=19;
     int cptcode=0;
 /***********************************************/    cptcoveff=0; 
 /**************** Main Program *****************/   
 /***********************************************/    for (k=0; k<maxncov; k++) Ndum[k]=0;
     for (k=1; k<=7; k++) ncodemax[k]=0;
 int main(int argc, char *argv[])  
 {    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;                                 modality*/ 
   double agedeb, agefin,hf;        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
   double agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;        Ndum[ij]++; /*store the modality */
         /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
   double fret;        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
   double **xi,tmp,delta;                                         Tvar[j]. If V=sex and male is 0 and 
                                          female is 1, then  cptcode=1.*/
   double dum; /* Dummy variable */      }
   double ***p3mat;  
   int *indx;      for (i=0; i<=cptcode; i++) {
   char line[MAXLINE], linepar[MAXLINE];        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
   char title[MAXLINE];      }
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];  
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];      ij=1; 
        for (i=1; i<=ncodemax[j]; i++) {
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];        for (k=0; k<= maxncov; k++) {
           if (Ndum[k] != 0) {
   char filerest[FILENAMELENGTH];            nbcode[Tvar[j]][ij]=k; 
   char fileregp[FILENAMELENGTH];            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   char popfile[FILENAMELENGTH];            
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];            ij++;
   int firstobs=1, lastobs=10;          }
   int sdeb, sfin; /* Status at beginning and end */          if (ij > ncodemax[j]) break; 
   int c,  h , cpt,l;        }  
   int ju,jl, mi;      } 
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    }  
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;  
   int mobilav=0,popforecast=0;   for (k=0; k< maxncov; k++) Ndum[k]=0;
   int hstepm, nhstepm;  
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1;   for (i=1; i<=ncovmodel-2; i++) { 
      /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   double bage, fage, age, agelim, agebase;     ij=Tvar[i];
   double ftolpl=FTOL;     Ndum[ij]++;
   double **prlim;   }
   double *severity;  
   double ***param; /* Matrix of parameters */   ij=1;
   double  *p;   for (i=1; i<= maxncov; i++) {
   double **matcov; /* Matrix of covariance */     if((Ndum[i]!=0) && (i<=ncovcol)){
   double ***delti3; /* Scale */       Tvaraff[ij]=i; /*For printing */
   double *delti; /* Scale */       ij++;
   double ***eij, ***vareij;     }
   double **varpl; /* Variances of prevalence limits by age */   }
   double *epj, vepp;   
   double kk1, kk2;   cptcoveff=ij-1; /*Number of simple covariates*/
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;  }
    
   /*********** Health Expectancies ****************/
   char version[80]="Imach version 0.71c, March 2002, INED-EUROREVES ";  
   char *alph[]={"a","a","b","c","d","e"}, str[4];  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   
   {
   char z[1]="c", occ;    /* Health expectancies, no variances */
 #include <sys/time.h>    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
 #include <time.h>    int nhstepma, nstepma; /* Decreasing with age */
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    double age, agelim, hf;
      double ***p3mat;
   /* long total_usecs;    double eip;
   struct timeval start_time, end_time;  
      pstamp(ficreseij);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
     fprintf(ficreseij,"# Age");
     for(i=1; i<=nlstate;i++){
   printf("\n%s",version);      for(j=1; j<=nlstate;j++){
   if(argc <=1){        fprintf(ficreseij," e%1d%1d ",i,j);
     printf("\nEnter the parameter file name: ");      }
     scanf("%s",pathtot);      fprintf(ficreseij," e%1d. ",i);
   }    }
   else{    fprintf(ficreseij,"\n");
     strcpy(pathtot,argv[1]);  
   }    
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    if(estepm < stepm){
   /*cygwin_split_path(pathtot,path,optionfile);      printf ("Problem %d lower than %d\n",estepm, stepm);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    }
   /* cutv(path,optionfile,pathtot,'\\');*/    else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);     * This is mainly to measure the difference between two models: for example
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);     * if stepm=24 months pijx are given only every 2 years and by summing them
   chdir(path);     * we are calculating an estimate of the Life Expectancy assuming a linear 
   replace(pathc,path);     * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
 /*-------- arguments in the command line --------*/     * estimate the model with stepm=1 month, we can keep estepm to 24 months
      * to compare the new estimate of Life expectancy with the same linear 
   strcpy(fileres,"r");     * hypothesis. A more precise result, taking into account a more precise
   strcat(fileres, optionfilefiname);     * curvature will be obtained if estepm is as small as stepm. */
   strcat(fileres,".txt");    /* Other files have txt extension */  
     /* For example we decided to compute the life expectancy with the smallest unit */
   /*---------arguments file --------*/    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
   if((ficpar=fopen(optionfile,"r"))==NULL)    {       nstepm is the number of stepm from age to agelin. 
     printf("Problem with optionfile %s\n",optionfile);       Look at hpijx to understand the reason of that which relies in memory size
     goto end;       and note for a fixed period like estepm months */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
   strcpy(filereso,"o");       means that if the survival funtion is printed only each two years of age and if
   strcat(filereso,fileres);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   if((ficparo=fopen(filereso,"w"))==NULL) {       results. So we changed our mind and took the option of the best precision.
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    */
   }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   
   /* Reads comments: lines beginning with '#' */    agelim=AGESUP;
   while((c=getc(ficpar))=='#' && c!= EOF){    /* If stepm=6 months */
     ungetc(c,ficpar);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     fgets(line, MAXLINE, ficpar);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
     puts(line);      
     fputs(line,ficparo);  /* nhstepm age range expressed in number of stepm */
   }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   ungetc(c,ficpar);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);  
 while((c=getc(ficpar))=='#' && c!= EOF){    for (age=bage; age<=fage; age ++){ 
     ungetc(c,ficpar);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
     fgets(line, MAXLINE, ficpar);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     puts(line);      /* if (stepm >= YEARM) hstepm=1;*/
     fputs(line,ficparo);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   }  
   ungetc(c,ficpar);      /* If stepm=6 months */
        /* Computed by stepm unit matrices, product of hstepma matrices, stored
             in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   covar=matrix(0,NCOVMAX,1,n);      
   cptcovn=0;      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   ncovmodel=2+cptcovn;      
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   /* Read guess parameters */      
   /* Reads comments: lines beginning with '#' */      /* Computing expectancies */
   while((c=getc(ficpar))=='#' && c!= EOF){      for(i=1; i<=nlstate;i++)
     ungetc(c,ficpar);        for(j=1; j<=nlstate;j++)
     fgets(line, MAXLINE, ficpar);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     puts(line);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     fputs(line,ficparo);            
   }            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   ungetc(c,ficpar);  
            }
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)      fprintf(ficreseij,"%3.0f",age );
     for(j=1; j <=nlstate+ndeath-1; j++){      for(i=1; i<=nlstate;i++){
       fscanf(ficpar,"%1d%1d",&i1,&j1);        eip=0;
       fprintf(ficparo,"%1d%1d",i1,j1);        for(j=1; j<=nlstate;j++){
       printf("%1d%1d",i,j);          eip +=eij[i][j][(int)age];
       for(k=1; k<=ncovmodel;k++){          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
         fscanf(ficpar," %lf",&param[i][j][k]);        }
         printf(" %lf",param[i][j][k]);        fprintf(ficreseij,"%9.4f", eip );
         fprintf(ficparo," %lf",param[i][j][k]);      }
       }      fprintf(ficreseij,"\n");
       fscanf(ficpar,"\n");      
       printf("\n");    }
       fprintf(ficparo,"\n");    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }    printf("\n");
      fprintf(ficlog,"\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    
   }
   p=param[1][1];  
    void cvevsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){  {
     ungetc(c,ficpar);    /* Covariances of health expectancies eij and of total life expectancies according
     fgets(line, MAXLINE, ficpar);     to initial status i, ei. .
     puts(line);    */
     fputs(line,ficparo);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   }    int nhstepma, nstepma; /* Decreasing with age */
   ungetc(c,ficpar);    double age, agelim, hf;
     double ***p3matp, ***p3matm, ***varhe;
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    double **dnewm,**doldm;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    double *xp, *xm;
   for(i=1; i <=nlstate; i++){    double **gp, **gm;
     for(j=1; j <=nlstate+ndeath-1; j++){    double ***gradg, ***trgradg;
       fscanf(ficpar,"%1d%1d",&i1,&j1);    int theta;
       printf("%1d%1d",i,j);  
       fprintf(ficparo,"%1d%1d",i1,j1);    double eip, vip;
       for(k=1; k<=ncovmodel;k++){  
         fscanf(ficpar,"%le",&delti3[i][j][k]);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
         printf(" %le",delti3[i][j][k]);    xp=vector(1,npar);
         fprintf(ficparo," %le",delti3[i][j][k]);    xm=vector(1,npar);
       }    dnewm=matrix(1,nlstate*nlstate,1,npar);
       fscanf(ficpar,"\n");    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
       printf("\n");    
       fprintf(ficparo,"\n");    pstamp(ficresstdeij);
     }    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   }    fprintf(ficresstdeij,"# Age");
   delti=delti3[1][1];    for(i=1; i<=nlstate;i++){
        for(j=1; j<=nlstate;j++)
   /* Reads comments: lines beginning with '#' */        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficresstdeij," e%1d. ",i);
     ungetc(c,ficpar);    }
     fgets(line, MAXLINE, ficpar);    fprintf(ficresstdeij,"\n");
     puts(line);  
     fputs(line,ficparo);    pstamp(ficrescveij);
   }    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   ungetc(c,ficpar);    fprintf(ficrescveij,"# Age");
      for(i=1; i<=nlstate;i++)
   matcov=matrix(1,npar,1,npar);      for(j=1; j<=nlstate;j++){
   for(i=1; i <=npar; i++){        cptj= (j-1)*nlstate+i;
     fscanf(ficpar,"%s",&str);        for(i2=1; i2<=nlstate;i2++)
     printf("%s",str);          for(j2=1; j2<=nlstate;j2++){
     fprintf(ficparo,"%s",str);            cptj2= (j2-1)*nlstate+i2;
     for(j=1; j <=i; j++){            if(cptj2 <= cptj)
       fscanf(ficpar," %le",&matcov[i][j]);              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
       printf(" %.5le",matcov[i][j]);          }
       fprintf(ficparo," %.5le",matcov[i][j]);      }
     }    fprintf(ficrescveij,"\n");
     fscanf(ficpar,"\n");    
     printf("\n");    if(estepm < stepm){
     fprintf(ficparo,"\n");      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
   for(i=1; i <=npar; i++)    else  hstepm=estepm;   
     for(j=i+1;j<=npar;j++)    /* We compute the life expectancy from trapezoids spaced every estepm months
       matcov[i][j]=matcov[j][i];     * This is mainly to measure the difference between two models: for example
         * if stepm=24 months pijx are given only every 2 years and by summing them
   printf("\n");     * we are calculating an estimate of the Life Expectancy assuming a linear 
      * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
     /*-------- Rewriting paramater file ----------*/     * estimate the model with stepm=1 month, we can keep estepm to 24 months
      strcpy(rfileres,"r");    /* "Rparameterfile */     * to compare the new estimate of Life expectancy with the same linear 
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/     * hypothesis. A more precise result, taking into account a more precise
      strcat(rfileres,".");    /* */     * curvature will be obtained if estepm is as small as stepm. */
      strcat(rfileres,optionfilext);    /* Other files have txt extension */  
     if((ficres =fopen(rfileres,"w"))==NULL) {    /* For example we decided to compute the life expectancy with the smallest unit */
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     }       nhstepm is the number of hstepm from age to agelim 
     fprintf(ficres,"#%s\n",version);       nstepm is the number of stepm from age to agelin. 
           Look at hpijx to understand the reason of that which relies in memory size
     /*-------- data file ----------*/       and note for a fixed period like estepm months */
     if((fic=fopen(datafile,"r"))==NULL)    {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       printf("Problem with datafile: %s\n", datafile);goto end;       survival function given by stepm (the optimization length). Unfortunately it
     }       means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     n= lastobs;       results. So we changed our mind and took the option of the best precision.
     severity = vector(1,maxwav);    */
     outcome=imatrix(1,maxwav+1,1,n);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     num=ivector(1,n);  
     moisnais=vector(1,n);    /* If stepm=6 months */
     annais=vector(1,n);    /* nhstepm age range expressed in number of stepm */
     moisdc=vector(1,n);    agelim=AGESUP;
     andc=vector(1,n);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     agedc=vector(1,n);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     cod=ivector(1,n);    /* if (stepm >= YEARM) hstepm=1;*/
     weight=vector(1,n);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    
     mint=matrix(1,maxwav,1,n);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     anint=matrix(1,maxwav,1,n);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     s=imatrix(1,maxwav+1,1,n);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     adl=imatrix(1,maxwav+1,1,n);        trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     tab=ivector(1,NCOVMAX);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     ncodemax=ivector(1,8);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
     i=1;    for (age=bage; age<=fage; age ++){ 
     while (fgets(line, MAXLINE, fic) != NULL)    {      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       if ((i >= firstobs) && (i <=lastobs)) {      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
              /* if (stepm >= YEARM) hstepm=1;*/
         for (j=maxwav;j>=1;j--){      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  
           strcpy(line,stra);      /* If stepm=6 months */
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
         }      
              hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);      /* Computing  Variances of health expectancies */
       /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);         decrease memory allocation */
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         for (j=ncov;j>=1;j--){          xm[i] = x[i] - (i==theta ?delti[theta]:0);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        }
         }        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         num[i]=atol(stra);        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
            
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){        for(j=1; j<= nlstate; j++){
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/          for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
         i=i+1;              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
       }              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
     }            }
     /* printf("ii=%d", ij);          }
        scanf("%d",i);*/        }
   imx=i-1; /* Number of individuals */       
         for(ij=1; ij<= nlstate*nlstate; ij++)
   /* for (i=1; i<=imx; i++){          for(h=0; h<=nhstepm-1; h++){
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;          }
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;      }/* End theta */
     }      
       
     for (i=1; i<=imx; i++)      for(h=0; h<=nhstepm-1; h++)
     if (covar[1][i]==0) printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/        for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
   /* Calculation of the number of parameter from char model*/            trgradg[h][j][theta]=gradg[h][theta][j];
   Tvar=ivector(1,15);      
   Tprod=ivector(1,15);  
   Tvaraff=ivector(1,15);       for(ij=1;ij<=nlstate*nlstate;ij++)
   Tvard=imatrix(1,15,1,2);        for(ji=1;ji<=nlstate*nlstate;ji++)
   Tage=ivector(1,15);                varhe[ij][ji][(int)age] =0.;
      
   if (strlen(model) >1){       printf("%d|",(int)age);fflush(stdout);
     j=0, j1=0, k1=1, k2=1;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     j=nbocc(model,'+');       for(h=0;h<=nhstepm-1;h++){
     j1=nbocc(model,'*');        for(k=0;k<=nhstepm-1;k++){
     cptcovn=j+1;          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     cptcovprod=j1;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
              for(ij=1;ij<=nlstate*nlstate;ij++)
                for(ji=1;ji<=nlstate*nlstate;ji++)
     strcpy(modelsav,model);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){        }
       printf("Error. Non available option model=%s ",model);      }
       goto end;  
     }      /* Computing expectancies */
          hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     for(i=(j+1); i>=1;i--){      for(i=1; i<=nlstate;i++)
       cutv(stra,strb,modelsav,'+');        for(j=1; j<=nlstate;j++)
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
       /*scanf("%d",i);*/            
       if (strchr(strb,'*')) {            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
         cutv(strd,strc,strb,'*');  
         if (strcmp(strc,"age")==0) {          }
           cptcovprod--;  
           cutv(strb,stre,strd,'V');      fprintf(ficresstdeij,"%3.0f",age );
           Tvar[i]=atoi(stre);      for(i=1; i<=nlstate;i++){
           cptcovage++;        eip=0.;
             Tage[cptcovage]=i;        vip=0.;
             /*printf("stre=%s ", stre);*/        for(j=1; j<=nlstate;j++){
         }          eip += eij[i][j][(int)age];
         else if (strcmp(strd,"age")==0) {          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
           cptcovprod--;            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           cutv(strb,stre,strc,'V');          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
           Tvar[i]=atoi(stre);        }
           cptcovage++;        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
           Tage[cptcovage]=i;      }
         }      fprintf(ficresstdeij,"\n");
         else {  
           cutv(strb,stre,strc,'V');      fprintf(ficrescveij,"%3.0f",age );
           Tvar[i]=ncov+k1;      for(i=1; i<=nlstate;i++)
           cutv(strb,strc,strd,'V');        for(j=1; j<=nlstate;j++){
           Tprod[k1]=i;          cptj= (j-1)*nlstate+i;
           Tvard[k1][1]=atoi(strc);          for(i2=1; i2<=nlstate;i2++)
           Tvard[k1][2]=atoi(stre);            for(j2=1; j2<=nlstate;j2++){
           Tvar[cptcovn+k2]=Tvard[k1][1];              cptj2= (j2-1)*nlstate+i2;
           Tvar[cptcovn+k2+1]=Tvard[k1][2];              if(cptj2 <= cptj)
           for (k=1; k<=lastobs;k++)                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];            }
           k1++;        }
           k2=k2+2;      fprintf(ficrescveij,"\n");
         }     
       }    }
       else {    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
        /*  scanf("%d",i);*/    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       cutv(strd,strc,strb,'V');    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       Tvar[i]=atoi(strc);    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       }    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       strcpy(modelsav,stra);      printf("\n");
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    fprintf(ficlog,"\n");
         scanf("%d",i);*/  
     }    free_vector(xm,1,npar);
 }    free_vector(xp,1,npar);
      free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   printf("cptcovprod=%d ", cptcovprod);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   scanf("%d ",i);*/  }
     fclose(fic);  
   /************ Variance ******************/
     /*  if(mle==1){*/  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
     if (weightopt != 1) { /* Maximisation without weights*/  {
       for(i=1;i<=n;i++) weight[i]=1.0;    /* Variance of health expectancies */
     }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /*-calculation of age at interview from date of interview and age at death -*/    /* double **newm;*/
     agev=matrix(1,maxwav,1,imx);    double **dnewm,**doldm;
     double **dnewmp,**doldmp;
    for (i=1; i<=imx; i++)    int i, j, nhstepm, hstepm, h, nstepm ;
      for(m=2; (m<= maxwav); m++)    int k, cptcode;
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    double *xp;
          anint[m][i]=9999;    double **gp, **gm;  /* for var eij */
          s[m][i]=-1;    double ***gradg, ***trgradg; /*for var eij */
        }    double **gradgp, **trgradgp; /* for var p point j */
        double *gpp, *gmp; /* for var p point j */
     for (i=1; i<=imx; i++)  {    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    double ***p3mat;
       for(m=1; (m<= maxwav); m++){    double age,agelim, hf;
         if(s[m][i] >0){    double ***mobaverage;
           if (s[m][i] == nlstate+1) {    int theta;
             if(agedc[i]>0)    char digit[4];
               if(moisdc[i]!=99 && andc[i]!=9999)    char digitp[25];
               agev[m][i]=agedc[i];  
             else {    char fileresprobmorprev[FILENAMELENGTH];
               if (andc[i]!=9999){  
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    if(popbased==1){
               agev[m][i]=-1;      if(mobilav!=0)
               }        strcpy(digitp,"-populbased-mobilav-");
             }      else strcpy(digitp,"-populbased-nomobil-");
           }    }
           else if(s[m][i] !=9){ /* Should no more exist */    else 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);      strcpy(digitp,"-stablbased-");
             if(mint[m][i]==99 || anint[m][i]==9999)  
               agev[m][i]=1;    if (mobilav!=0) {
             else if(agev[m][i] <agemin){      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
               agemin=agev[m][i];      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
             }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
             else if(agev[m][i] >agemax){      }
               agemax=agev[m][i];    }
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/  
             }    strcpy(fileresprobmorprev,"prmorprev"); 
             /*agev[m][i]=anint[m][i]-annais[i];*/    sprintf(digit,"%-d",ij);
             /*   agev[m][i] = age[i]+2*m;*/    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
           }    strcat(fileresprobmorprev,digit); /* Tvar to be done */
           else { /* =9 */    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
             agev[m][i]=1;    strcat(fileresprobmorprev,fileres);
             s[m][i]=-1;    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
           }      printf("Problem with resultfile: %s\n", fileresprobmorprev);
         }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
         else /*= 0 Unknown */    }
           agev[m][i]=1;    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       }   
        fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     }    pstamp(ficresprobmorprev);
     for (i=1; i<=imx; i++)  {    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
       for(m=1; (m<= maxwav); m++){    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
         if (s[m][i] > (nlstate+ndeath)) {    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           printf("Error: Wrong value in nlstate or ndeath\n");        fprintf(ficresprobmorprev," p.%-d SE",j);
           goto end;      for(i=1; i<=nlstate;i++)
         }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
       }    }  
     }    fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
     free_vector(severity,1,maxwav);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     free_imatrix(outcome,1,maxwav+1,1,n);  /*   } */
     free_vector(moisnais,1,n);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_vector(annais,1,n);    pstamp(ficresvij);
     /* free_matrix(mint,1,maxwav,1,n);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
        free_matrix(anint,1,maxwav,1,n);*/    if(popbased==1)
     free_vector(moisdc,1,n);      fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
     free_vector(andc,1,n);    else
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
        fprintf(ficresvij,"# Age");
     wav=ivector(1,imx);    for(i=1; i<=nlstate;i++)
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      for(j=1; j<=nlstate;j++)
     mw=imatrix(1,lastpass-firstpass+1,1,imx);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
        fprintf(ficresvij,"\n");
     /* Concatenates waves */  
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
       Tcode=ivector(1,100);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       ncodemax[1]=1;  
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
          gpp=vector(nlstate+1,nlstate+ndeath);
    codtab=imatrix(1,100,1,10);    gmp=vector(nlstate+1,nlstate+ndeath);
    h=0;    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
    m=pow(2,cptcoveff);    
      if(estepm < stepm){
    for(k=1;k<=cptcoveff; k++){      printf ("Problem %d lower than %d\n",estepm, stepm);
      for(i=1; i <=(m/pow(2,k));i++){    }
        for(j=1; j <= ncodemax[k]; j++){    else  hstepm=estepm;   
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    /* For example we decided to compute the life expectancy with the smallest unit */
            h++;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
            if (h>m) h=1;codtab[h][k]=j;       nhstepm is the number of hstepm from age to agelim 
          }       nstepm is the number of stepm from age to agelin. 
        }       Look at hpijx to understand the reason of that which relies in memory size
      }       and note for a fixed period like k years */
    }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
    /*for(i=1; i <=m ;i++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
      for(k=1; k <=cptcovn; k++){       results. So we changed our mind and took the option of the best precision.
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);    */
      }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
      printf("\n");    agelim = AGESUP;
    }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
    scanf("%d",i);*/      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
          nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
    /* Calculates basic frequencies. Computes observed prevalence at single age      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        and prints on file fileres'p'. */      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
          gm=matrix(0,nhstepm,1,nlstate);
      
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(theta=1; theta <=npar; theta++){
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        }
              hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     /* For Powell, parameters are in a vector p[] starting at p[1]        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */  
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */        if (popbased==1) {
           if(mobilav ==0){
     if(mle==1){            for(i=1; i<=nlstate;i++)
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);              prlim[i][i]=probs[(int)age][i][ij];
     }          }else{ /* mobilav */ 
                for(i=1; i<=nlstate;i++)
     /*--------- results files --------------*/              prlim[i][i]=mobaverage[(int)age][i][ij];
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, weightopt,model);          }
          }
     
    jk=1;        for(j=1; j<= nlstate; j++){
    fprintf(ficres,"# Parameters\n");          for(h=0; h<=nhstepm; h++){
    printf("# Parameters\n");            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
    for(i=1,jk=1; i <=nlstate; i++){              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
      for(k=1; k <=(nlstate+ndeath); k++){          }
        if (k != i)        }
          {        /* This for computing probability of death (h=1 means
            printf("%d%d ",i,k);           computed over hstepm matrices product = hstepm*stepm months) 
            fprintf(ficres,"%1d%1d ",i,k);           as a weighted average of prlim.
            for(j=1; j <=ncovmodel; j++){        */
              printf("%f ",p[jk]);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
              fprintf(ficres,"%f ",p[jk]);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
              jk++;            gpp[j] += prlim[i][i]*p3mat[i][j][1];
            }        }    
            printf("\n");        /* end probability of death */
            fprintf(ficres,"\n");  
          }        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
      }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
    }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
  if(mle==1){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     /* Computing hessian and covariance matrix */   
     ftolhess=ftol; /* Usually correct */        if (popbased==1) {
     hesscov(matcov, p, npar, delti, ftolhess, func);          if(mobilav ==0){
  }            for(i=1; i<=nlstate;i++)
     fprintf(ficres,"# Scales\n");              prlim[i][i]=probs[(int)age][i][ij];
     printf("# Scales\n");          }else{ /* mobilav */ 
      for(i=1,jk=1; i <=nlstate; i++){            for(i=1; i<=nlstate;i++)
       for(j=1; j <=nlstate+ndeath; j++){              prlim[i][i]=mobaverage[(int)age][i][ij];
         if (j!=i) {          }
           fprintf(ficres,"%1d%1d",i,j);        }
           printf("%1d%1d",i,j);  
           for(k=1; k<=ncovmodel;k++){        for(j=1; j<= nlstate; j++){
             printf(" %.5e",delti[jk]);          for(h=0; h<=nhstepm; h++){
             fprintf(ficres," %.5e",delti[jk]);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
             jk++;              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }          }
           printf("\n");        }
           fprintf(ficres,"\n");        /* This for computing probability of death (h=1 means
         }           computed over hstepm matrices product = hstepm*stepm months) 
       }           as a weighted average of prlim.
      }        */
            for(j=nlstate+1;j<=nlstate+ndeath;j++){
     k=1;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     fprintf(ficres,"# Covariance\n");           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     printf("# Covariance\n");        }    
     for(i=1;i<=npar;i++){        /* end probability of death */
       /*  if (k>nlstate) k=1;  
       i1=(i-1)/(ncovmodel*nlstate)+1;        for(j=1; j<= nlstate; j++) /* vareij */
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          for(h=0; h<=nhstepm; h++){
       printf("%s%d%d",alph[k],i1,tab[i]);*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       fprintf(ficres,"%3d",i);          }
       printf("%3d",i);  
       for(j=1; j<=i;j++){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
         fprintf(ficres," %.5e",matcov[i][j]);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         printf(" %.5e",matcov[i][j]);        }
       }  
       fprintf(ficres,"\n");      } /* End theta */
       printf("\n");  
       k++;      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     }  
          for(h=0; h<=nhstepm; h++) /* veij */
     while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate;j++)
       ungetc(c,ficpar);          for(theta=1; theta <=npar; theta++)
       fgets(line, MAXLINE, ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
       puts(line);  
       fputs(line,ficparo);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     }        for(theta=1; theta <=npar; theta++)
     ungetc(c,ficpar);          trgradgp[j][theta]=gradgp[theta][j];
      
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemaxpar, &bage, &fage);  
          hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     if (fage <= 2) {      for(i=1;i<=nlstate;i++)
       bage = agemin;        for(j=1;j<=nlstate;j++)
       fage = agemaxpar;          vareij[i][j][(int)age] =0.;
     }  
          for(h=0;h<=nhstepm;h++){
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");        for(k=0;k<=nhstepm;k++){
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemaxpar,bage,fage);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemaxpar,bage,fage);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
            for(i=1;i<=nlstate;i++)
     while((c=getc(ficpar))=='#' && c!= EOF){            for(j=1;j<=nlstate;j++)
     ungetc(c,ficpar);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
     fgets(line, MAXLINE, ficpar);        }
     puts(line);      }
     fputs(line,ficparo);    
   }      /* pptj */
   ungetc(c,ficpar);      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
        matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);      for(j=nlstate+1;j<=nlstate+ndeath;j++)
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          varppt[j][i]=doldmp[j][i];
            /* end ppptj */
   while((c=getc(ficpar))=='#' && c!= EOF){      /*  x centered again */
     ungetc(c,ficpar);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     fgets(line, MAXLINE, ficpar);      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     puts(line);   
     fputs(line,ficparo);      if (popbased==1) {
   }        if(mobilav ==0){
   ungetc(c,ficpar);          for(i=1; i<=nlstate;i++)
              prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
    dateprev1=anprev1+mprev1/12.+jprev1/365.;          for(i=1; i<=nlstate;i++)
    dateprev2=anprev2+mprev2/12.+jprev2/365.;            prlim[i][i]=mobaverage[(int)age][i][ij];
         }
   fscanf(ficpar,"pop_based=%d\n",&popbased);      }
   fprintf(ficparo,"pop_based=%d\n",popbased);                 
   fprintf(ficres,"pop_based=%d\n",popbased);        /* This for computing probability of death (h=1 means
           computed over hstepm (estepm) matrices product = hstepm*stepm months) 
   while((c=getc(ficpar))=='#' && c!= EOF){         as a weighted average of prlim.
     ungetc(c,ficpar);      */
     fgets(line, MAXLINE, ficpar);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
     puts(line);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     fputs(line,ficparo);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   }      }    
   ungetc(c,ficpar);      /* end probability of death */
   
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
 while((c=getc(ficpar))=='#' && c!= EOF){        }
     ungetc(c,ficpar);      } 
     fgets(line, MAXLINE, ficpar);      fprintf(ficresprobmorprev,"\n");
     puts(line);  
     fputs(line,ficparo);      fprintf(ficresvij,"%.0f ",age );
   }      for(i=1; i<=nlstate;i++)
   ungetc(c,ficpar);        for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);        }
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      fprintf(ficresvij,"\n");
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
 /*------------ gnuplot -------------*/      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, agemin,agemaxpar,fage, pathc,p);    } /* End age */
      free_vector(gpp,nlstate+1,nlstate+ndeath);
 /*------------ free_vector  -------------*/    free_vector(gmp,nlstate+1,nlstate+ndeath);
  chdir(path);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
      free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
  free_ivector(wav,1,imx);    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
  free_ivector(num,1,n);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
  free_vector(agedc,1,n);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
  /*free_matrix(covar,1,NCOVMAX,1,n);*/  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
  fclose(ficparo);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
  fclose(ficres);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
 /*--------- index.htm --------*/    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres);    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
    /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
   /*--------------- Prevalence limit --------------*/    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
    
   strcpy(filerespl,"pl");    free_vector(xp,1,npar);
   strcat(filerespl,fileres);    free_matrix(doldm,1,nlstate,1,nlstate);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    free_matrix(dnewm,1,nlstate,1,npar);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   }    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   fprintf(ficrespl,"#Prevalence limit\n");    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   fprintf(ficrespl,"#Age ");    fclose(ficresprobmorprev);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    fflush(ficgp);
   fprintf(ficrespl,"\n");    fflush(fichtm); 
    }  /* end varevsij */
   prlim=matrix(1,nlstate,1,nlstate);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /************ Variance of prevlim ******************/
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  {
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* Variance of prevalence limit */
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   k=0;    double **newm;
   agebase=agemin;    double **dnewm,**doldm;
   agelim=agemaxpar;    int i, j, nhstepm, hstepm;
   ftolpl=1.e-10;    int k, cptcode;
   i1=cptcoveff;    double *xp;
   if (cptcovn < 1){i1=1;}    double *gp, *gm;
     double **gradg, **trgradg;
   for(cptcov=1;cptcov<=i1;cptcov++){    double age,agelim;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    int theta;
         k=k+1;    
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    pstamp(ficresvpl);
         fprintf(ficrespl,"\n#******");    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
         for(j=1;j<=cptcoveff;j++)    fprintf(ficresvpl,"# Age");
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for(i=1; i<=nlstate;i++)
         fprintf(ficrespl,"******\n");        fprintf(ficresvpl," %1d-%1d",i,i);
            fprintf(ficresvpl,"\n");
         for (age=agebase; age<=agelim; age++){  
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    xp=vector(1,npar);
           fprintf(ficrespl,"%.0f",age );    dnewm=matrix(1,nlstate,1,npar);
           for(i=1; i<=nlstate;i++)    doldm=matrix(1,nlstate,1,nlstate);
           fprintf(ficrespl," %.5f", prlim[i][i]);    
           fprintf(ficrespl,"\n");    hstepm=1*YEARM; /* Every year of age */
         }    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
       }    agelim = AGESUP;
     }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   fclose(ficrespl);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
   /*------------- h Pij x at various ages ------------*/      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
        gradg=matrix(1,npar,1,nlstate);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      gp=vector(1,nlstate);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      gm=vector(1,nlstate);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  
   }      for(theta=1; theta <=npar; theta++){
   printf("Computing pij: result on file '%s' \n", filerespij);        for(i=1; i<=npar; i++){ /* Computes gradient */
            xp[i] = x[i] + (i==theta ?delti[theta]:0);
   stepsize=(int) (stepm+YEARM-1)/YEARM;        }
   /*if (stepm<=24) stepsize=2;*/        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
   agelim=AGESUP;          gp[i] = prlim[i][i];
   hstepm=stepsize*YEARM; /* Every year of age */      
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */        for(i=1; i<=npar; i++) /* Computes gradient */
            xp[i] = x[i] - (i==theta ?delti[theta]:0);
   k=0;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   for(cptcov=1;cptcov<=i1;cptcov++){        for(i=1;i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          gm[i] = prlim[i][i];
       k=k+1;  
         fprintf(ficrespij,"\n#****** ");        for(i=1;i<=nlstate;i++)
         for(j=1;j<=cptcoveff;j++)          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      } /* End theta */
         fprintf(ficrespij,"******\n");  
              trgradg =matrix(1,nlstate,1,npar);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for(j=1; j<=nlstate;j++)
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        for(theta=1; theta <=npar; theta++)
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          trgradg[j][theta]=gradg[theta][j];
           oldm=oldms;savm=savms;  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        for(i=1;i<=nlstate;i++)
           fprintf(ficrespij,"# Age");        varpl[i][(int)age] =0.;
           for(i=1; i<=nlstate;i++)      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
             for(j=1; j<=nlstate+ndeath;j++)      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
               fprintf(ficrespij," %1d-%1d",i,j);      for(i=1;i<=nlstate;i++)
           fprintf(ficrespij,"\n");        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
           for (h=0; h<=nhstepm; h++){  
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      fprintf(ficresvpl,"%.0f ",age );
             for(i=1; i<=nlstate;i++)      for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);      fprintf(ficresvpl,"\n");
             fprintf(ficrespij,"\n");      free_vector(gp,1,nlstate);
           }      free_vector(gm,1,nlstate);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      free_matrix(gradg,1,npar,1,nlstate);
           fprintf(ficrespij,"\n");      free_matrix(trgradg,1,nlstate,1,npar);
         }    } /* End age */
     }  
   }    free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/    free_matrix(dnewm,1,nlstate,1,nlstate);
   
   fclose(ficrespij);  }
   
   /************ Variance of one-step probabilities  ******************/
   /*---------- Forecasting ------------------*/  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   if((stepm == 1) && (strcmp(model,".")==0)){  {
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);    int i, j=0,  i1, k1, l1, t, tj;
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    int k2, l2, j1,  z1;
     free_matrix(mint,1,maxwav,1,n);    int k=0,l, cptcode;
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    int first=1, first1;
     free_vector(weight,1,n);}    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
   else{    double **dnewm,**doldm;
     erreur=108;    double *xp;
     printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model);    double *gp, *gm;
   }    double **gradg, **trgradg;
      double **mu;
     double age,agelim, cov[NCOVMAX];
   /*---------- Health expectancies and variances ------------*/    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
   strcpy(filerest,"t");    char fileresprob[FILENAMELENGTH];
   strcat(filerest,fileres);    char fileresprobcov[FILENAMELENGTH];
   if((ficrest=fopen(filerest,"w"))==NULL) {    char fileresprobcor[FILENAMELENGTH];
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  
   }    double ***varpij;
   printf("Computing Total LEs with variances: file '%s' \n", filerest);  
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
   strcpy(filerese,"e");    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   strcat(filerese,fileres);      printf("Problem with resultfile: %s\n", fileresprob);
   if((ficreseij=fopen(filerese,"w"))==NULL) {      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    }
   }    strcpy(fileresprobcov,"probcov"); 
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
  strcpy(fileresv,"v");      printf("Problem with resultfile: %s\n", fileresprobcov);
   strcat(fileresv,fileres);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    }
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    strcpy(fileresprobcor,"probcor"); 
   }    strcat(fileresprobcor,fileres);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
   k=0;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   for(cptcov=1;cptcov<=i1;cptcov++){    }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
       k=k+1;    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
       fprintf(ficrest,"\n#****** ");    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
       for(j=1;j<=cptcoveff;j++)    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
       fprintf(ficrest,"******\n");    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
       fprintf(ficreseij,"\n#****** ");    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresprob,"# Age");
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    pstamp(ficresprobcov);
       fprintf(ficreseij,"******\n");    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
       fprintf(ficresvij,"\n#****** ");    pstamp(ficresprobcor);
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    fprintf(ficresprobcor,"# Age");
       fprintf(ficresvij,"******\n");  
   
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    for(i=1; i<=nlstate;i++)
       oldm=oldms;savm=savms;      for(j=1; j<=(nlstate+ndeath);j++){
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);          fprintf(ficresprob," p%1d-%1d (SE)",i,j);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       oldm=oldms;savm=savms;        fprintf(ficresprobcor," p%1d-%1d ",i,j);
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      }  
       /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
      fprintf(ficresprobcor,"\n");
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");   */
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);   xp=vector(1,npar);
       fprintf(ficrest,"\n");    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
       hf=1;    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
       if (stepm >= YEARM) hf=stepm/YEARM;    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
       epj=vector(1,nlstate+1);    first=1;
       for(age=bage; age <=fage ;age++){    fprintf(ficgp,"\n# Routine varprob");
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
         if (popbased==1) {    fprintf(fichtm,"\n");
           for(i=1; i<=nlstate;i++)  
             prlim[i][i]=probs[(int)age][i][k];    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
         }    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
            file %s<br>\n",optionfilehtmcov);
         fprintf(ficrest," %.0f",age);    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){  and drawn. It helps understanding how is the covariance between two incidences.\
           for(i=1, epj[j]=0.;i <=nlstate;i++) {   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
           }  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
           epj[nlstate+1] +=epj[j];  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
         }  standard deviations wide on each axis. <br>\
         for(i=1, vepp=0.;i <=nlstate;i++)   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
           for(j=1;j <=nlstate;j++)   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
             vepp += vareij[i][j][(int)age];  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));  
         for(j=1;j <=nlstate;j++){    cov[1]=1;
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    tj=cptcoveff;
         }    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
         fprintf(ficrest,"\n");    j1=0;
       }    for(t=1; t<=tj;t++){
     }      for(i1=1; i1<=ncodemax[t];i1++){ 
   }        j1++;
         if  (cptcovn>0) {
   fclose(ficreseij);          fprintf(ficresprob, "\n#********** Variable "); 
   fclose(ficresvij);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   fclose(ficrest);          fprintf(ficresprob, "**********\n#\n");
   fclose(ficpar);          fprintf(ficresprobcov, "\n#********** Variable "); 
   free_vector(epj,1,nlstate+1);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprobcov, "**********\n#\n");
   /*------- Variance limit prevalence------*/            
           fprintf(ficgp, "\n#********** Variable "); 
   strcpy(fileresvpl,"vpl");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcat(fileresvpl,fileres);          fprintf(ficgp, "**********\n#\n");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {          
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          
     exit(0);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   }          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
   k=0;          fprintf(ficresprobcor, "\n#********** Variable ");    
   for(cptcov=1;cptcov<=i1;cptcov++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          fprintf(ficresprobcor, "**********\n#");    
       k=k+1;        }
       fprintf(ficresvpl,"\n#****** ");        
       for(j=1;j<=cptcoveff;j++)        for (age=bage; age<=fage; age ++){ 
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          cov[2]=age;
       fprintf(ficresvpl,"******\n");          for (k=1; k<=cptcovn;k++) {
                  cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
       varpl=matrix(1,nlstate,(int) bage, (int) fage);          }
       oldm=oldms;savm=savms;          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);          for (k=1; k<=cptcovprod;k++)
     }            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
  }          
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   fclose(ficresvpl);          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
   /*---------- End : free ----------------*/          gm=vector(1,(nlstate)*(nlstate+ndeath));
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      
            for(theta=1; theta <=npar; theta++){
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);            for(i=1; i<=npar; i++)
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
              
              pmij(pmmij,cov,ncovmodel,xp,nlstate);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);            
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);            k=0;
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);            for(i=1; i<= (nlstate); i++){
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);              for(j=1; j<=(nlstate+ndeath);j++){
                  k=k+1;
   free_matrix(matcov,1,npar,1,npar);                gp[k]=pmmij[i][j];
   free_vector(delti,1,npar);              }
   free_matrix(agev,1,maxwav,1,imx);            }
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);            
             for(i=1; i<=npar; i++)
   if(erreur >0)              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
     printf("End of Imach with error %d\n",erreur);      
   else   printf("End of Imach\n");            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */            k=0;
              for(i=1; i<=(nlstate); i++){
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/              for(j=1; j<=(nlstate+ndeath);j++){
   /*printf("Total time was %d uSec.\n", total_usecs);*/                k=k+1;
   /*------ End -----------*/                gm[k]=pmmij[i][j];
               }
             }
  end:       
 #ifdef windows            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
   /* chdir(pathcd);*/              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
 #endif          }
  /*system("wgnuplot graph.plt");*/  
  /*system("../gp37mgw/wgnuplot graph.plt");*/          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
  /*system("cd ../gp37mgw");*/            for(theta=1; theta <=npar; theta++)
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/              trgradg[j][theta]=gradg[theta][j];
  strcpy(plotcmd,GNUPLOTPROGRAM);          
  strcat(plotcmd," ");          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
  strcat(plotcmd,optionfilegnuplot);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
  system(plotcmd);          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
 #ifdef windows          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   while (z[0] != 'q') {          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
     chdir(path);  
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          pmij(pmmij,cov,ncovmodel,x,nlstate);
     scanf("%s",z);          
     if (z[0] == 'c') system("./imach");          k=0;
     else if (z[0] == 'e') {          for(i=1; i<=(nlstate); i++){
       chdir(path);            for(j=1; j<=(nlstate+ndeath);j++){
       system(optionfilehtm);              k=k+1;
     }              mu[k][(int) age]=pmmij[i][j];
     else if (z[0] == 'q') exit(0);            }
   }          }
 #endif          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
 }            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, (b) health expectancies by health status at initial age:  ei., eij . If one or more covariate are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), eij are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences (i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char  *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %d %s for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
           exit(1);
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           exit(1);
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         exit(1);
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line,j);
         exit(1);
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         exit(1);
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           exit(1);
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       } 
       lstra=strlen(stra);
       
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
     fclose(fic);
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
     /* for (i=1; i<=imx; i++) */
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
       
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /*---------- Health expectancies and variances ------------*/
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficreseij,"\n#****** ");
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
           cvevsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav, strstart);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav, strstart);
           }
   
           pstamp(ficrest);
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n# Age ( e.. (std) ");
           for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
           fprintf(ficrest,"\n");
   
           epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             if (popbased==1) {
               if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=probs[(int)age][i][k];
               }else{ /* mobilav */ 
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=mobaverage[(int)age][i][k];
               }
             }
           
             fprintf(ficrest," %4.0f",age);
             for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
               for(i=1, epj[j]=0.;i <=nlstate;i++) {
                 epj[j] += prlim[i][i]*eij[i][j][(int)age];
                 /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
               }
               epj[nlstate+1] +=epj[j];
             }
   
             for(i=1, vepp=0.;i <=nlstate;i++)
               for(j=1;j <=nlstate;j++)
                 vepp += vareij[i][j][(int)age];
             fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
             for(j=1;j <=nlstate;j++){
               fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
             }
             fprintf(ficrest,"\n");
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficreseij);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.32  
changed lines
  Added in v.1.126


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